<PAGE>   1

================================================================================

                       SECURITIES AND EXCHANGE COMMISSION

                              Washington, DC 20549

                         -------------------------------

                                    FORM 10-Q

         [X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
             EXCHANGE ACT OF 1934

         For the quarterly period ended              JULY 31, 1999
                                        ----------------------------------------

         [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
             EXCHANGE ACT OF 1934

         For the transition period from _______________to_______________________

                  Commission File Number               001-15167
                                        ----------------------------------------



                               BIOPURE CORPORATION
             (Exact name of registrant as specified in its charter)

                Delaware                                 04-2836871
        (State of Incorporation)            (IRS Employer Identification Number)

11 Hurley Street, Cambridge, Massachusetts                  02141
 (Address of  principal executive offices)                (Zip Code)

                                 (617) 234-6500
                         (Registrant's telephone number)

                         -------------------------------

Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days. Yes [ ] No [X]

Indicate the number of shares outstanding of each of the issuer's classes of
common stock as of August 27, 1999.

                  Class A Common Stock, $.01 par value ...........22,280,867
                  Class B Common Stock, $1.00 par value ...............117.7

================================================================================
<PAGE>   2






                               BIOPURE CORPORATION

                               INDEX TO FORM 10-Q

<TABLE>
<CAPTION>
                                                                                 Page
                                                                                 ----

<S>                                                                              <C>
Part I - Financial Information:

     Item 1 - Financial Statements (Unaudited)

             Condensed Consolidated Balance Sheets at
             July 31, 1999 and October 31, 1998                                   1-2

             Condensed Consolidated Statements of Operations
             for the quarters ended July 31, 1999 and August 1, 1998 and
             for the nine months ended July 31, 1999 and August 1, 1998             3

             Condensed Consolidated Statements of Cash Flows
             for the nine months ended July 31, 1999 and August 1, 1998             4

             Notes to Condensed Consolidated Financial Statements                 5-7

    Item 2 - Management's Discussion and Analysis of Financial Condition
             and Results of Operations                                           8-11

    Item 3 - Quantitative and Qualitative Disclosure of Market Risk                12


Part II - Other Information:

    Item 1 - Legal Proceedings                                                     13

    Item 2 - Changes in Securities and Use of Proceeds                             13

    Item 4 - Submission of Matters to a Vote of Security Holders                   13

    Item 6 - Exhibits and Reports on Form 8-K                                      13

Signatures                                                                         14

Exhibit Index
</TABLE>

<PAGE>   3

                                                                       FORM 10-Q
                                                                       PART 1
                                                                       ITEM 1
                                                                       PAGE 1

                               BIOPURE CORPORATION

                      Condensed Consolidated Balance Sheets
                (In thousands, except share and per share data)
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                                    July 31, 1999       October 31, 1998
                                                                    -------------       ----------------
<S>                                                                    <C>                   <C>
Assets:
Current assets:
     Cash and cash equivalents                                         $ 7,995               $ 6,063
     Accounts receivable, net                                              393                   346
     Inventories, net                                                    4,370                 3,072
     Subscription receivable from underwriters                          39,060                    --
     Current portion of restricted cash                                  3,508                 3,508
     Other current assets                                                  186                   186
                                                                       -------               -------
           Total current assets                                         55,512                13,175

Property, plant and equipment, net                                      28,330                29,606
Investment in affiliate                                                    131                   131
Other assets                                                             1,494                 1,936
                                                                       -------               -------
            Total assets                                               $85,467               $44,848
                                                                       =======               =======

Liabilities and stockholders' equity:
Current liabilities:
     Accounts payable                                                  $   691               $ 1,523
     Accrued expenses                                                    9,475                 7,666
     Current portion of long-term debt                                   4,500                 2,000
                                                                       -------               -------
           Total current liabilities                                    14,666                11,189

Long-term debt                                                              --                 4,000
Deferred compensation                                                    1,772                 1,910
Common stock to be repurchased (1,694,273
  shares of Class A Common Stock at July 31, 1999
  and 2,013,956 at October 31,1998)                                      5,300                 6,300

Stockholders' equity:
     Convertible preferred stock, $0.01 par value,
       30,000,000 shares authorized at July 31, 1999
       and 9,000,000 at October 31, 1998
       Series A, no shares outstanding at
         July 31, 1999 and 346,663 at
         October 31, 1998                                                   --                     3
       Series B, no shares outstanding at
         July 31, 1999 and 2,127,251 at
         October 31, 1998                                                   --                    22
       Series C, no shares outstanding at July 31, 1999
         and 2,830,188 at October 31, 1998                                  --                    28
     Common stock:
       Class A, $0.01 par value, 100,000,000 shares
         authorized at July 31, 1999 and 40,000,000
         at October 31, 1998, 22,280,867 shares
         outstanding at July 31, 1999 and 10,539,225
         at October 31, 1998                                               223                   107
       Class B, $1.00 par value, 179 shares
         authorized, 117.7 shares outstanding                               --                    --
</TABLE>





<PAGE>   4

                                                                       FORM 10-Q
                                                                       PART 1
                                                                       ITEM 1
                                                                       PAGE 2

                               BIOPURE CORPORATION

                      Condensed Consolidated Balance Sheets
                (In thousands, except share and per share data)
                                   (Unaudited)
                                   (Continued)

Capital in excess of par value                         281,747          197,495
Contributed capital                                     24,574           24,574
Notes receivable                                        (2,429)          (2,291)
Treasury stock, at cost (no shares
  of Class A Common Stock at July 31,
  1999 and 203,278 at October 31, 1998)                     --           (1,583)
Accumulated deficit                                   (240,386)        (196,906)
                                                     ---------        ---------
      Total stockholders' equity                        63,729           21,449
                                                     ---------        ---------
        Total liabilities and stockholders'
        equity                                       $  85,467        $  44,848
                                                     =========        =========


Note: The balance sheet at October 31, 1998 has been derived from the audited
financial statements at that date but does not include all of the information
and footnotes required by generally accepted accounting principles for complete
financial statements.

                             See accompanying notes.


<PAGE>   5


                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 1
                                                                       PAGE 3

                               BIOPURE CORPORATION

                 Condensed Consolidated Statements of Operations
                     (In thousands, except per share data)
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                        Three Months Ended                  Nine Months Ended
                                                    --------------------------          --------------------------
                                                    July 31,         August 1,          July 31,         August 1,
                                                      1999             1998               1999             1998
                                                    --------         ---------          --------         ---------
<S>                                                 <C>              <C>                <C>              <C>
Revenues:
        Oxyglobin                                   $    641         $    253           $  2,122         $    377
        Other                                             --               28                 64              118
                                                    --------         --------           --------         --------
                  Total revenues                         641              281              2,186              495
Cost of revenues                                       1,741               --              4,970               --
                                                    --------         --------           --------         --------
Gross profit (loss)                                   (1,100)             281             (2,784)             495

Operating expenses:
        Research and development                       7,449            5,120             17,320           17,205
        Sales and marketing                              724              573              2,236            1,642
        General and administrative                     1,158            1,166              3,572            3,185
                                                    --------         --------           --------         --------
                 Total operating expenses              9,331            6,859             23,128           22,032
                                                    --------         --------           --------         --------

Loss from operations                                 (10,431)          (6,578)           (25,912)         (21,537)

Other income (expense)                                    88              (63)               347              402
                                                    --------         --------           --------         --------

Net loss                                             (10,343)          (6,641)           (25,565)         (21,135)
Stock dividends on preferred stock                   (17,915)              --            (17,915)              --
                                                    --------         --------           --------         --------
Net loss applicable to
common stockholders                                 $(28,258)         $(6,641)          $(43,480)        $(21,135)
                                                    ========         ========           ========         ========

Historical:
        Basic net loss
        per common share                            $  (2.29)        $  (0.53)          $  (3.53)        $  (1.70)

        Weighted average shares used in
        computing basic net loss
        per common share                              12,328           12,465             12,331           12,439

Pro forma:
        Pro forma basic net loss
        per common share                            $  (1.38)        $  (0.36)          $  (2.21)        $  (1.16)

        Weighted average shares used in
        computing pro forma basic net
        loss per common share                         20,496           18,405             19,669           18,161
</TABLE>



                             See accompanying notes.


<PAGE>   6


                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 1
                                                                       PAGE 4

                               BIOPURE CORPORATION

                 Condensed Consolidated Statement of Cash Flows
                                 (In thousands)
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                                                     Nine Months Ended
                                                                             ------------------------------------
                                                                             July 31, 1999         August 1, 1998
                                                                             -------------         --------------

<S>                                                                             <C>                   <C>
Operating activities:
     Net loss                                                                   $(25,565)             $(21,135)

Adjustments to reconcile net loss to net
  cash used in operating activities:
     Depreciation                                                                  2,927                 2,417
     Equity compensation                                                              67                   276
     Deferred compensation                                                          (138)                  158
     Accrued interest on stockholders' notes receivable                             (137)                 (135)
     Accounts receivable                                                             (47)                 (113)
     Inventories                                                                  (1,298)               (2,690)
     Other current assets                                                           (339)                   32
     Accounts payable                                                               (832)                  175
     Accrued expenses                                                                767                  (394)
                                                                                --------              --------

              Net cash used in operating activities                              (24,595)              (21,409)

Investing activities:
     Purchase of property, plant and equipment                                    (1,652)               (4,230)
     Other assets                                                                    442                  (141)
     Restricted cash                                                                  --                (2,392)
                                                                                --------              --------
             Net cash used in investing activities                                (1,210)               (6,763)

Financing activities:
     Net proceeds from sale of common stock                                           --                 1,764
     Net proceeds from sale of preferred stock                                    30,149                28,209
     Payment of long-term debt                                                    (1,500)               (1,500)
     Repurchase of common stock                                                   (1,000)                   --
     Proceeds from exercise of options                                                88                    68
                                                                                --------              --------
            Net cash provided by financing activities                             27,737                28,541

Net increase in cash and cash equivalents                                          1,932                   369

Cash and cash equivalents at beginning of period                                   6,063                13,527
                                                                                --------              --------
Cash and cash equivalents at end of period                                      $  7,995              $ 13,896
                                                                                ========              ========
</TABLE>





                             See accompanying notes.


<PAGE>   7


                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 1
                                                                       PAGE 5

                               BIOPURE CORPORATION

              Notes to Condensed Consolidated Financial Statements
                                  July 31, 1999
                                   (Unaudited)

1. BASIS OF PRESENTATION

           The accompanying unaudited condensed consolidated financial
           statements have been prepared in accordance with generally accepted
           accounting principles for interim financial information and pursuant
           to the rules and regulations of the Securities and Exchange
           Commission (SEC). Accordingly, they do not include all of the
           information and footnotes required by generally accepted accounting
           principles for complete financial statements.

           In the opinion of management, all adjustments (consisting of normal
           recurring adjustments) considered necessary for a fair presentation
           have been included. Operating results for the three and nine months
           periods ended July 31, 1999 are not necessarily indicative of the
           results that may be expected for the year ended October 31, 1999.

           For further information, refer to the consolidated financial
           statements and footnotes thereto for the year ended October 31, 1998,
           included in the Company's Registration Statement on Form S-1,
           Registration No. 333-78829.

2. INITIAL PUBLIC OFFERING

           On July 21, 1999 the Class A Common Stock was combined on a
           two-for-three basis. This combination has been retroactively
           reflected in the accompanying consolidated financial statements.

           On July 29, 1999 Biopure entered into an agreement for the initial
           public offering (IPO) of 3,500,000 shares of Class A Common Stock at
           a price of $12 per share, less an underwriting discount, and on
           August 4, 1999 the Company received $39,060,000 of proceeds from the
           offering, before estimated expenses of $1,358,000. As of July 31,
           1999 we recorded a subscription receivable from underwriters of
           $39,060,000 and an increase in stockholders' equity of $37,702,000
           for the estimated net proceeds of the offering and accrued $1,126,000
           for expenses of the offering. Upon the closing of the IPO, all shares
           of preferred stock converted into shares of Class A Common Stock.
           This conversion of preferred stock into common stock has been
           reflected in the equity section of the balance sheet as if it had
           occurred as of July 31, 1999.

3. NET LOSS PER SHARE

           Historical basic net loss per share is computed based on the
           weighted-average number of common shares outstanding during the
           period. Diluted net loss per share is computed based upon the
           weighted-average number of common shares outstanding during the year,
           adjusted for the dilutive effect of shares issuable upon the
           conversion of preferred stock outstanding and the exercise of common
           stock options and warrants determined based upon the average market
           price of common stock for the period. Diluted net loss per share is
           not presented in the accompanying condensed consolidated financial
           statements because the Company had losses for all periods presented.

           The pro forma basic net loss per common share is computed using the
           weighted-average number of outstanding common shares assuming
           conversion of all convertible preferred shares into common shares at
           date of original issuance.

           Subsequent to May 20, 1999, an additional 93,750 units of Series D
           Convertible Preferred Stock were sold with aggregate net proceeds of
           $1,125,000. In accordance with the provisions of EITF 98-5, for


<PAGE>   8

                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 1
                                                                       PAGE 6

                               BIOPURE CORPORATION

              Notes to Condensed Consolidated Financial Statements
                                  July 31, 1999
                                   (Unaudited)
                                   (Continued)

           those units sold after May 20, 1999, the Company treated any shares
           of Class A Common Stock issued upon conversion in excess of
           two-thirds of one share of Class A Common Stock for each share of
           Series D Convertible Preferred Stock as a dividend for accounting
           purposes. The Company recorded a dividend of $155,000 in the third
           quarter of 1999.

           The holders of the Series B and Series C Convertible Preferred Stock
           agreed to convert their shares at the time of the Company's IPO on
           the condition that the holders of the Series B Convertible Preferred
           Stock receive an additional 280,000 shares in the aggregate upon
           conversion and the holders of the Series C Convertible Preferred
           Stock receive an additional 1,200,000 shares in the aggregate upon
           conversion. The fair market value of such additional shares has been
           treated, for accounting purposes, as a dividend. Consequently, the
           Company recorded a dividend of $17,760,000 in the third quarter of
           1999.

           The following table sets forth the computation of basic and pro forma
           loss per share for the three and nine months ended July 31, 1999 and
           August 1, 1998 (in thousands, except per share data):

<TABLE>
<CAPTION>
                                                                      Three Months Ended            Nine Months Ended
                                                                   ------------------------      -----------------------
                                                                   July 31,       August 1,      July 31,      August 1,
                                                                     1999           1998           1999           1998
                                                                   --------       ---------      --------      ---------
             <S>                                                   <C>            <C>            <C>           <C>
             Historical:
                Net loss                                           $(10,343)      $ (6,641)      $(25,565)     $(21,135)
                Stock dividends on
                  preferred stock                                   (17,915)            --        (17,915)            --
                                                                   --------       --------       --------       --------

            Net loss applicable to
            common stockholders                                    $(28,258)      $ (6,641)      $(43,480)      $(21,135)
                                                                   ========       ========       ========       ========

            Weighted-average number of
            common shares outstanding                                12,328         12,465         12,331         12,439
                                                                   ========       ========       ========       ========

            Basic net loss
            per common share                                       $  (2.29)      $  (0.53)      $  (3.53)      $  (1.70)
                                                                   ========       ========       ========       ========

            Pro forma:
              Weighted-average number of
               common shares:
                  Historical outstanding                             12,328         12,465         12,331         12,439
                  Issued upon conversion
                  of preferred stock                                  8,168          5,940          7,338          5,722
                                                                   --------       --------       --------       --------
                      Total weighted-average number
                      of common shares used in
                      computing pro forma basic net
                      loss per common share                          20,496         18,405         19,669         18,161
                                                                   ========       ========       ========       ========

           Pro forma basic net loss
           per common share                                        $  (1.38)      $  (0.36)      $  (2.21)      $  (1.16)
                                                                   ========       ========       ========       ========
</TABLE>


<PAGE>   9


                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 1
                                                                       PAGE 7

                               BIOPURE CORPORATION

              Notes to Condensed Consolidated Financial Statements
                                  July 31, 1999
                                   (Unaudited)
                                   (Continued)

4.   INVENTORIES

           Inventories are valued at the lower of cost (determined using the
           first-in, first-out method) or market. Inventories were as follows
           (in thousands):

<TABLE>
<CAPTION>
                                                           July 31, 1999        October 31, 1998
                                                           -------------        ----------------

           <S>                                                 <C>                    <C>
           Raw materials ................................      $1,094                 $  935
           Work-in-process ..............................         416                    542
           Finished goods ...............................       2,860                  1,595
                                                               ------                 ------
                                                               $4,370                 $3,072
                                                               ======                 ======
</TABLE>

5.   LITIGATION

     The Company is a party to litigation initially filed in 1990 arising from
     certain joint venture agreements for development and distribution of
     product in Central and South America. Summary judgments were entered
     against the two plaintiffs in 1994. The plaintiffs each appealed the
     judgments; one of the appeals was voluntarily dismissed. The other appeal
     was denied in part and remanded to the trial court for further findings
     based on lack of jurisdiction. It is anticipated that the trial court will
     make the requisite findings in the calendar year 1999. In connection with
     the summary judgments, the Company agreed to a settlement with a
     third-party intervenor with claims against one of the plaintiffs. Final
     payment of the settlement is subject to the outcome of the pending appeal;
     however, the Company has provided for such settlement in the accompanying
     consolidated financial statements. At July 31, 1999, the Company had
     $3,508,000 in escrow in connection with this settlement and included this
     amount in other current assets. The settlement amount has been recorded as
     a current obligation.


<PAGE>   10


                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 2
                                                                       PAGE 8

                               BIOPURE CORPORATION

                     Management's Discussion and Analysis of
                  Financial Condition and Results of Operations
                                  July 31, 1999

Except for historical information contained herein, some matters discussed in
this report constitute forward-looking statements within the meaning of Section
27A of the Securities Act of 1933, as amended, and Section 21E of the Securities
Exchange Act of 1934, as amended. Actual results could differ materially from
those projected in the forward-looking statements as a result of the risk
factors set forth in this report and in the Company's Registration Statement
(Form S-1, Registration No. 333-78829) and Prospectus dated July 29, 1999. In
light of the substantial risks and uncertainties inherent in all future
projections, the inclusion of forward-looking statements in this report should
not be regarded as representations by the Company that the objectives or plans
of the Company will be achieved. Many factors could cause the Company's actual
results, performance or achievements to differ materially from those in the
forward-looking statements. Reference is made in particular to the discussions
set forth below in this Report under "Management's Discussion and Analysis of
Financial Condition and Results of Operations," and set forth in the
Registration Statement (Form S-1, Registration No. 333-78829) and Prospectus'
under the captions "Risk Factors" and "Management's Discussion and Analysis of
Financial Condition and Results of Operations."

RESULTS OF OPERATIONS

THREE MONTHS ENDED JULY 31, 1999 COMPARED TO THREE MONTHS ENDED AUGUST 1, 1998

Total revenues increased 128.1% to $641,000 in the third quarter of fiscal 1999
from $281,000 in the third quarter of fiscal 1998. Revenues in the third quarter
of fiscal 1999 consisted of Oxyglobin (veterinary product) sales.

Cost of revenues was $1,741,000 in the third quarter of fiscal 1999. We did not
recognize any cost of revenues in the third quarter of fiscal 1998. All such
costs during the third quarter of 1998 were allocated to research and
development expenses prior to FDA approval of Oxyglobin in March 1998 and while
we expanded manufacturing capacity following FDA approval.

Research and development expenses increased 45.5% to $7,449,000 in the third
quarter of fiscal 1999 from $5,120,000 in the third quarter of fiscal 1998. This
increase was primarily attributable to increased Phase III clinical trial
activity and pre-clinical activity related to our human oxygen therapeutic
product, Hemopure, partially offset by the allocation of that portion of
manufacturing expenses associated with the production of Oxyglobin to cost of
revenues.

Sales and marketing expenses increased 26.6% to $724,000 in the third quarter of
fiscal 1999 from $573,000 in the third quarter of fiscal 1998. This increase was
primarily attributable to increased sales and marketing personnel and selling,
marketing and distribution expenses related to Oxyglobin.

Total other income (expense) was income of $88,000 in the third quarter of
fiscal 1999 compared to an expense of $63,000 in the third quarter of fiscal
1998. This favorable change of $151,000 was primarily associated with $208,000
of other expenses incurred in the third quarter of fiscal 1998 associated with a
discontinued development project unrelated to oxygen therapeutics.

Basic net loss per common share for the quarter was $2.29, compared with a basic
net loss per common share of $0.53 for the same period in 1998. The pro forma
basic net loss per common share was $1.38, compared with $0.36 for the same
period in 1998. The 1999 historic and pro forma basic net loss per common share
include a one-time loss of $1.45 and $0.87, respectively, associated with
$17,915,000 in common stock dividends issued to preferred stockholders.



<PAGE>   11

                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 2
                                                                       PAGE 9

                               BIOPURE CORPORATION

                     Management's Discussion and Analysis of
                  Financial Condition and Results of Operations
                                  July 31, 1999
                                   (Continued)

NINE MONTHS ENDED JULY 31, 1999 COMPARED TO NINE MONTHS ENDED AUGUST 1, 1998

Total revenues increased 341.6% to $2,186,000 in the first nine months of fiscal
1999 from $495,000 in the first nine months of fiscal 1998. Revenues in the
first nine months of fiscal 1999 include $2,122,000 of Oxyglobin sales.
Oxyglobin sales commenced in mid-March of fiscal 1998 to a discrete number of
emergency and specialty practices in the United States. We launched Oxyglobin in
the United States in October 1998.

Cost of revenues was $4,970,000 in the first nine months of fiscal 1999. We did
not realize any cost of revenues in the first nine months of fiscal 1998. Cost
of revenues in the first nine months in fiscal 1999 reflects the allocation of a
portion of the manufacturing costs associated with the production of Oxyglobin.
These costs were entirely allocated to research and development expenses prior
to August 1998.

Research and development expenses increased 0.7% to $17,320,000 in the first
nine months of fiscal 1999 from $17,205,000 in the first nine months of fiscal
1998. This increase was primarily attributable to increased Phase III clinical
trial activity and pre-clinical activity related to our human oxygen therapeutic
product, Hemopure, largely offset by the allocation of manufacturing expenses
associated with the production of Oxyglobin to cost of revenues.

Sales and marketing expenses increased 36.2% to $2,236,000 in the first nine
months of fiscal 1999 from $1,642,000 in the first nine months of fiscal 1998.
This increase was primarily attributable to increased sales and marketing
personnel, as well as selling, advertising, marketing and distribution expenses
related to Oxyglobin.

General and administrative expenses increased 12.2% to $3,572,000 in the first
nine months of fiscal 1999 from $3,185,000 in the first nine months of fiscal
1998. This was attributable to increased management personnel and intellectual
property related legal fees and was partially offset by decreased market
research and public relations activities.

Total other income, net, decreased by 13.7% to $347,000 in the first nine months
of fiscal 1999 compared to $402,000 in the first nine months of fiscal 1998.
This decrease of $55,000 was primarily attributable to a $667,000 decrease in
interest income associated with lower average cash balances. Partially
offsetting this reduction in interest income was a $204,000 reduction in
interest expense associated with a lower long-term debt balance. Additionally,
$200,000 of other income was realized in the nine months of fiscal 1999 as
compared to $208,000 of other expense realized in the nine months of fiscal
1998, both of which were associated with a discontinued development project
unrelated to oxygen therapeutics.

Basic net loss per common share for the 1999 nine month period was $3.53,
compared with $1.70 for the same period in 1998. The pro forma basic net loss
per common share was $2.21, compared with $1.16 for the same period in 1998. For
the 1999 nine month period, the historic and pro forma basic net loss per common
share include a one-time loss of $1.45 and $0.91, respectively, associated with
$17,915,000 in common stock dividends issued to preferred stockholders.



<PAGE>   12


                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 2
                                                                       PAGE 10

                               BIOPURE CORPORATION

                     Management's Discussion and Analysis of
                  Financial Condition and Results of Operations
                                  July 31, 1999
                                   (Continued)

LIQUIDITY AND CAPITAL RESOURCES

At July 31, 1999, we had current assets of $55,512,000, which consisted
primarily of $7,995,000 in cash and cash equivalents, $4,370,000 in net
inventory and $39,060,000 in subscription receivable from underwriters related
to shares of common stock sold through our initial public offering. At July 31,
1999, current liabilities were $14,666,000.

We have financed operations from inception primarily through sales of equity
securities, development and license agreement payments, interest income and
debt.

In December 1998 and April and May 1999 we sold Series D Convertible Preferred
Stock with aggregate net proceeds of $30,149,000. In July 1999, we sold
3,500,000 shares of Class A Common Stock in our IPO with total net proceeds of
$37,702,000. Our primary investment objective is preservation of principal and
currently we invest in high-grade commercial paper and money market funds which
are intended to minimize risks of interest rate changes.

In October 1996, we incurred $9,000,000 in long-term debt to Pharmacia & Upjohn,
Inc. in connection with the mutual termination of a strategic alliance. As of
July 31, 1999, we had repaid $4,500,000 of the principal amount of this debt.
The $4,500,000 outstanding principal balance became payable upon the completion
of our IPO and has been reflected in current liabilities at July 31, 1999.

On August 5, 1999 the Company paid $4,000,000 which was in addition to an
existing balance of $1,000,000 in an escrow account to complete the August 9,
1999 repurchase of 1,694,273 shares of our Class A Common Stock from a
stockholder.

We have not been profitable since inception and had an accumulated deficit of
$240,386,000 as of July 31, 1999. We will continue to generate losses from
operations for the foreseeable future. We will explore opportunities to raise
capital through sales of equity and debt securities, potential partnerships,
bank borrowings or leasing arrangements.

We believe our current cash, cash equivalents and short-term investments, should
be more than sufficient to meet our projected requirements for the next twelve
months including the anticipated completion of our pivotal Phase III trial. Our
cash requirements may vary significantly from current projections.

As of October 31, 1998, we had net operating loss carryforwards of approximately
$140,000,000 to offset future federal and state taxable income through 2013. Due
to the degree of uncertainty related to the ultimate realization of such prior
losses, no benefit has been recognized in our financial statements as of October
31, 1998. Utilization of such losses in future years may be limited under the
change of stock ownership rules of the Internal Revenue Service.


<PAGE>   13


                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 2
                                                                       PAGE 11

                               BIOPURE CORPORATION

                     Management's Discussion and Analysis of
                  Financial Condition and Results of Operations
                                  July 31, 1999
                                   (Continued)

YEAR 2000 COMPLIANCE

Some currently installed computer systems and software products are coded to
accept or recognize only two digit entries in the date code field. These systems
and software products will need to accept four digit entries to distinguish 21st
century dates from 20th century dates. As a result, computer systems and
software used by many companies and governmental agencies may need to be
upgraded to comply with such Year 2000 requirements or risk system failure or
miscalculations causing disruptions of normal business activities.

STATE OF READINESS
We have made an assessment of the ability of our critical information and
non-information systems to function properly with respect to dates in the year
2000 and thereafter. We have based this assessment upon communications with
equipment and software vendors, literature supplied with software and in
connection with maintenance contracts and test evaluations of our systems. Our
critical systems are defined as: transactional systems affecting product
manufacturing, delivery and quality; systems which play an infrastructure role
in supporting our business and scientific operations; and systems which use
forward-looking or date-based forecasting such as sample or batch expiration
dates.

We have identified potential problems in some of our critical systems and began
repairing, upgrading or replacing such systems in the second quarter of fiscal
1999. We expect to complete this process by the end of the fourth quarter of
fiscal 1999. We expect to repair, replace or upgrade non-critical systems by the
end of calendar year 1999. We will continue to monitor and remediate our
critical and non-critical systems.

COSTS
To date, we have incurred, or are committed to incur, approximately $85,000 in
costs in connection with identifying and evaluating Year 2000 compliance issues.
Most of our expenses generally relate to, and are expected to continue to relate
to, the operating costs associated with time spent by employees in the
assessment process, the repair, upgrade or replacement process and Year 2000
compliance matters. We estimate that the total cost of our Year 2000 project
will be $300,000 and intend to expense such costs as they are incurred. We
expect to fund all of these expenses from working capital. In the event that we
incur expenses higher than anticipated, such additional expenses could harm our
business.

RISKS
We have also commenced an assessment of the Year 2000 risks of our key
suppliers, including contract research organizations working on our clinical
trials, vendors and veterinary distributors of Oxyglobin. Our assessment is
based upon questionnaires submitted to and Year 2000 disclosures received from
these third parties. We believe that any Year 2000 risks associated with these
third parties will not have a material effect on our business. We base our
beliefs on the following facts: our key suppliers, vendors and veterinary
distributors are in the process of upgrading to Year 2000-compliant systems, and
our clinical trial information that might be sensitive to the change from 1999
to 2000 is minimal.

CONTINGENCY PLAN
In the event that we do not complete our Year 2000 conversion, we will manually
perform those tasks which would otherwise be performed by our non-Year
2000-compliant systems until such systems are repaired, upgraded or replaced. In
this event, we anticipate that we may experience delays in our production runs.


<PAGE>   14

                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 3
                                                                       PAGE 12

                               BIOPURE CORPORATION

                     Management's Discussion and Analysis of
                  Financial Condition and Results of Operations
                                  July 31, 1999
                                   (Continued)

QUANTITATIVE AND QUALITATIVE DISCLOSURE OF MARKET RISK

The Company currently does not have any foreign currency exchange risks with the
exception of negligible exchange fluctuations associated with expenses for
clinical trial and regulatory activities outside of the United States. The
Company invests its cash and cash equivalents in high-grade commercial paper and
money market funds.


<PAGE>   15
                                                                       FORM 10-Q
                                                                       PART II
                                                                       ITEM 1-6
                                                                       PAGE 13

                               BIOPURE CORPORATION
                           Part II - Other Information
                                  July 31, 1999

ITEM 1 - LEGAL PROCEEDINGS

Reference is made to "Business - Litigation" in Registration Statement
No. 333-78829.

ITEM 2 - CHANGES IN SECURITIES AND USE OF PROCEEDS

During the third fiscal quarter ended July 31, 1999, the Corporation sold
397,250 shares of Series D Convertible Preferred Stock ("Series D Stock") with
warrants to purchase one share of Class A Common Stock for each 15 shares of
Series D Stock acquired. Sales were completed May 13 through May 27, 1999. The
securities were sold to accredited investors, as defined in Regulation D under
the Securities Act of 1933. The price per unit was $12.00. Aggregate
commissions were $78,750.

The Corporation relied upon Section 4(2) of the Securities Act of 1933
following the requirements described in Securities Act Rule 506 and
Regulation D.

By its terms the Series D Stock sold in May 1999 was automatically convertible
upon consummation of an initial public offering at a ratio related to (a) the
initial public offering price to the public and (b) the period of time the
Series D Stock was outstanding. The Series D Stock converted into Class A Common
Stock on August 4, 1999 at conversion ratios of 0.815, 0.810 and 0.805 for
Series D Stock issued on May 13, May 20 and May 27, 1999 respectively.


The Corporation's first registration statement, Registration No. 333-78829,
became effective July 29, 1999, and the offering commenced July 30, 1999. The
offering has terminated with the sale of all of the securities registered,
except for the underwriters' overallotment option.

The managing underwriters were J.P. Morgan and Co., Adams, Harkness & Hill, Inc.
and Robert W. Baird & Co. Incorporated.

The securities registered were 3,500,000 shares of Class A Common Stock, plus
575,000 additional shares to cover the underwriters' overallotment option. All
shares were registered for the account of the issuer.

The aggregate price of the offering amount registered and sold, not including
shares to cover the underwriters' overallotment option, was $42,000,000.

Expenses incurred in connection with the issuance and distribution of the
securities registered were as follows: for underwriting discounts and
commissions - $2,940,000; finders fees - $0; expenses paid to or for
underwriters - $0; other expenses - $1,358,000; and total expenses - $4,298,000.
Other expenses and total expenses are estimates. None of such payments were
direct or indirect payments to directors or officers of the issuer or their
associates or to persons owning 10 percent or more of any class of equity
securities of the issuer or any of its affiliates or direct or indirect payments
to others.

The net offering proceeds to the issuer after deducting underwriters' discounts
and the total expenses described above were $37,702,000.

Following the effective date of the registration statement there remained one
business day in the period covered by this report. The Company did not receive
proceeds from the offering during the period.

ITEM 4 - SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

Two matters were submitted to a vote of security holders during the third fiscal
quarter ended July 31, 1999; (1) approval of the 1999 Omnibus Securities and
Incentive Plan (the "Omnibus Plan") and (2) approval of amendments to the
Corporation's Restated Certificate of Incorporation (the "Amendments").

         (1) As of July 9, 1999 the requisite amount of consents to the Omnibus
             Plan were attained with 11,238,544 votes for and 18,333 against.

         (2) As of July 21, 1999 the requisite amount of consents to the
             Amendments were attained with 14,818,170 votes for and 27,333
             against.

ITEM 6 - EXHIBITS AND REPORTS ON FORM 8-K

         (a) The exhibits are listed in the accompanying Exhibit Index.

         (b) No reports on Form 8-K were filed during the quarter for which
             this report is filed.


<PAGE>   16


                                                                       FORM 10-Q
                                                                       PART II
                                                                       PAGE 14

                                   SIGNATURES



Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.


                                             BIOPURE CORPORATION



         Date: September 14, 1999            By: /s/ Carl W. Rausch
                                                 ------------------------------
                                                 Carl W. Rausch
                                                 Chairman of the Board
                                                 Chief Executive Officer


         Date: September 14, 1999            By: /s/ Brian A. Lajoie
                                                 ------------------------------
                                                 Brian A. Lajoie
                                                 Vice President/Controller


<PAGE>   17







                                  EXHIBIT INDEX

Number                     Description
------                     -----------

3(i)                       Amended Restated Certificate of Incorporation

27.1                       Financial Data Schedule for nine months ended
                           July 31, 1999

27.2                       Financial Data Schedule for nine months ended
                           August 1, 1998

27.3                       Financial Data Schedule for three months ended
                           July 31, 1999

27.4                       Financial Data Schedule for three months ended
                           August 1, 1998