<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 29, 2000
                              -------------------------------------------------

     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 X No _

The number of shares outstanding of each of the issuer's classes of common stock
as of August 25, 2000 was:

         Class A Common Stock, $.01 par value............... 24,936,031
         Class B Common Stock, $1.00 par value..............      117.7

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

<PAGE>   2

                               BIOPURE CORPORATION

                               INDEX TO FORM 10-Q


                                                                            Page
                                                                            ----



Part I - Financial Information:

    Item 1 - Financial Statements (Unaudited)

           Condensed Consolidated Balance Sheets at
           July 29, 2000 and October 31, 1999                                 1

           Condensed Consolidated Statements of Operations
           for the quarters ended July 29, 2000 and July 31, 1999 and
           for the nine months ended July 29, 2000 and July 31, 1999          2

           Condensed Consolidated Statements of Cash Flows
           for the nine months ended July 29, 2000 and July 31, 1999          3

           Notes to Condensed Consolidated Financial
           Statements                                                       4-7


    Item 2 - Management's Discussion and Analysis of
             Financial Condition and Results of Operations                 8-10

    Item 3 - Quantitative and Qualitative Disclosure of Market Risk          11

Part II - Other Information:

    Item 1 -   Legal Proceedings                                             12

    Item 2 -   Changes in Securities and Use of Proceeds                     12

    Item 6 -   Exhibits and Reports on Form 8-K                              12

Signatures                                                                   13

Exhibit Index


<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>
Assets:                                                   July 29, 2000   October 31, 1999
                                                          -------------   ----------------
<S>                                                         <C>               <C>
Current assets:
    Cash and cash equivalents                               $  95,616         $  30,778
    Accounts receivable, net                                      381               321
    Inventories, net                                            3,089             3,182
    Current portion of restricted cash                          3,508             3,508
    Other current assets                                          555               488
                                                            ---------         ---------
         Total current assets                                 103,149            38,277

Property, plant and equipment, net                             24,398            27,447
Investment in affiliate                                           101               101
Other assets                                                      232               405
                                                            ---------         ---------
         Total assets                                       $ 127,880         $  66,230
                                                            =========         =========

Liabilities and stockholders' equity:
Current liabilities:
    Accounts payable                                        $   1,160         $     741
    Accrued expenses                                           11,557             9,664
                                                            ---------         ---------
    Total current liabilities                                  12,717            10,405

Deferred compensation                                           1,768             1,788

Stockholders' equity:
    Convertible preferred stock, $0.01 par value,
      30,000,000 shares authorized, no shares outstanding           -                 -
    Common stock:
      Class A, $0.01 par value, 100,000,000 shares
        authorized, 24,936,031 shares
        outstanding at July 29, 2000 and 22,280,867
        at October 31, 1999                                       249               223
      Class B, $1.00 par value, 179 shares
        authorized, 117.7 shares outstanding                        -                 -
    Capital in excess of par value                            370,230           282,054
    Contributed capital                                        24,574            24,574
    Notes receivable                                           (2,025)           (2,463)
    Accumulated deficit                                      (279,633)         (250,351)
                                                            ---------         ---------

Total stockholders' equity                                    113,395            54,037
                                                            ---------         ---------
         Total liabilities and stockholders'
          equity                                            $ 127,880         $  66,230
                                                            =========         =========
</TABLE>


Note: The balance sheet at October 31, 1999 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>   4

                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 1
                                                                       PAGE 2

                               BIOPURE CORPORATION

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


<TABLE>
<CAPTION>
                                      Three Months Ended      Nine Months Ended
                                     --------------------    --------------------
                                     July 29,    July 31,    July 29,    July 31,
                                       2000        1999        2000        1999
                                     --------    --------    --------    --------
<S>                                  <C>         <C>         <C>         <C>
Revenues:
   Oxyglobin                         $    836    $    641    $  2,140    $  2,122
   Other                                    -           -           3          64
                                     --------    --------    --------    --------
       Total revenues                     836         641       2,143       2,186
Cost of revenues                        1,215       1,741       3,506       4,970
                                     --------    --------    --------    --------
Gross profit (loss)                      (379)     (1,100)     (1,363)     (2,784)

Operating expenses:
   Research and development             6,229       7,449      22,631      17,320
   Sales and marketing                    617         724       1,765       2,236
   General and administrative           1,529       1,158       6,377       3,572
                                     --------    --------    --------    --------
   Total operating expenses             8,375       9,331      30,773      23,128
                                     --------    --------    --------    --------

Loss from operations                   (8,754)    (10,431)    (32,136)    (25,912)
Other income                            1,563          88       2,854         347
                                     --------    --------    --------    --------

Net loss                               (7,191)    (10,343)    (29,282)    (25,565)
Stock dividends on preferred stock          -     (17,915)          -     (17,915)
                                     --------    --------    --------    --------

Net loss applicable to
common stockholders                  $ (7,191)   $(28,258)   $(29,282)   $(43,480)
                                     ========    ========    ========    ========

Historical:
   Basic net loss
   per common share                  $  (0.29)   $  (2.29)   $  (1.24)   $  (3.53)

   Weighted average shares used in
   computing basic net loss
   per common share*                   24,933      12,328      23,605      12,331

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

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


                             See accompanying notes.

*Actual shares outstanding at July 29, 2000 were 24,936.

<PAGE>   5

                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 1
                                                                       PAGE 3

                               BIOPURE CORPORATION

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

<TABLE>
<CAPTION>
                                                               Nine Months Ended
                                                        -------------------------------
                                                        July 29, 2000     July 31, 1999
                                                        -------------     -------------
<S>                                                        <C>              <C>
Operating activities:
    Net loss                                               $(29,282)        $(25,565)

Adjustments to reconcile net loss to net
  cash used in operating activities:
    Depreciation                                              3,108            2,927
    Disposition of obsolete fixed assets                        331                -
    Equity compensation                                       1,785               67
    Deferred compensation                                       (20)            (138)
    Accrued interest on stockholders' notes receivable         (118)            (137)
    Accounts receivable                                         (60)             (47)
    Inventories                                                  93           (1,298)
    Other current assets                                        (67)            (339)
    Accounts payable                                            419             (832)
    Accrued expenses                                          1,893              767
                                                           --------         --------
       Net cash used in operating activities                (21,918)         (24,595)

Investing activities:
    Purchase of property, plant and equipment                  (390)          (1,652)
    Other assets                                                173              442
                                                           --------         --------
       Net cash used in investing activities                   (217)          (1,210)

Financing activities:
    Net proceeds from sale of common stock                   83,745                -
    Net proceeds from sale of preferred stock                     -           30,149
    Payment of long-term debt                                     -           (1,500)
    Repurchase of common stock                                    -           (1,000)
    Payment of notes receivable from shareholders               556                -
    Proceeds from exercise of options and warrants              560               88
    Proceeds from exercise of non lapse restricted stock      2,112                -
                                                           --------         --------
       Net cash provided by financing activities             86,973           27,737
                                                           --------         --------

Net increase in cash and cash equivalents                    64,838            1,932
Cash and cash equivalents at beginning of period             30,778            6,063
                                                           --------         --------
Cash and cash equivalents at end of period                 $ 95,616         $  7,995
                                                           ========         ========
</TABLE>

                             See accompanying notes.

<PAGE>   6

                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 1
                                                                       PAGE 4

                               BIOPURE CORPORATION

              Notes to Condensed Consolidated Financial Statements
                                  July 29, 2000
                                   (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 month periods
     ended July 29, 2000 are not necessarily indicative of the results that may
     be expected for the year ended October 31, 2000.

     For further information, refer to the consolidated financial statements and
     footnotes thereto for the year ended October 31, 1999, included in the
     Company's Annual Report on Form 10-K for the year ended October 31, 1999.


2. 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.

<PAGE>   7

                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 1
                                                                       PAGE 5

                               BIOPURE CORPORATION

              Notes to Condensed Consolidated Financial Statements
                                  July 29, 2000
                                   (Unaudited)
                                   (Continued)


The following table sets forth the computation of basic and pro forma loss per
share for the three and nine months ended July 29, 2000 and July 31, 1999 (in
thousands, except per share data):

<TABLE>
<CAPTION>
                                               Three Months Ended           Nine Months Ended
                                              --------------------        ----------------------
                                              July 29,    July 31,        July 29,      July 31,
                                                2000        1999            2000         1999
                                              --------    --------        --------      --------
<S>                                           <C>         <C>             <C>           <C>
Historical:
  Net loss                                    $ (7,191)   $(10,343)       $(29,282)     $(25,565)
  Stock dividends on
    preferred stock                                  -     (17,915)              -       (17,915)
                                              --------    --------        --------      --------

  Net loss applicable to
  common stockholders                         $ (7,191)   $(28,258)       $(29,282)     $(43,480)
                                              ========    ========        ========      ========

  Weighted-average number of
  common shares outstanding                     24,933      12,328          23,605        12,331
                                              ========    ========        ========      ========


Basic net loss
per common share                              $  (0.29)   $  (2.29)       $  (1.24)     $  (3.53)
                                              ========    ========        ========      ========

Pro forma:
  Weighted-average number of common shares:
    Historical outstanding                                  12,328                        12,331
    Issued upon conversion
    of preferred stock                                       8,168                         7,338
                                                          --------                      --------
    Total weighted-average number
    of common shares used in
    computing pro forma basic net
    loss per common share                                   20,496                        19,669
                                                          ========                      ========
Pro forma basic net loss
per common share                                          $  (1.38)                     $  (2.21)
                                                          ========                      ========

</TABLE>
<PAGE>   8

                                                                     FORM 10-Q
                                                                     PART I
                                                                     ITEM 1
                                                                     PAGE 6

                               BIOPURE CORPORATION

              Notes to Condensed Consolidated Financial Statements
                                  July 29, 2000
                                   (Unaudited)
                                   (Continued)


3. INVENTORIES

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

                                                July 29, 2000   October 31, 1999
                                                -------------   ----------------
     In thousands
     Raw materials ......................           $1,031           $  690
     Work-in-process ....................              770              134
     Finished goods .....................            1,288            2,358
                                                    ------           ------
                                                    $3,089           $3,182
                                                    ======           ======

4. ACCRUED EXPENSES

     Accrued expenses consisted of the following:


                                                July 29, 2000   October 31, 1999
                                                -------------   ----------------
     In thousands
     Settlement ............................       $ 3,508           $3,508
     Phase III clinical trial ..............         5,834            2,925
     Public Offering .......................             -              619
     Other .................................         2,215            2,612
                                                   -------           ------
                                                   $11,557           $9,664
                                                   =======           ======


5. STOCK OPTION COMPENSATION

     In August 1999, Biopure granted 386,680 options to two directors which,
     under the Interpretation of APB 25, are assumed to be for services in
     addition to board activities and must be accounted for at fair value. The
     Company records compensation expense based on the service period which
     ranges from two to four years adjusted for the fair value of the stock
     until the options have been earned as discussed below. In November 1999,
     Biopure granted 25,000 warrants to three consultants, which must be
     accounted for at fair value. With respect to these 411,680 options and
     warrants, $(34,000) and $1,786,000 were charged to non-cash compensation
     expense for the quarter ended and the nine months ended July 29, 2000,
     respectively.



<PAGE>   9

                                                                     FORM 10-Q
                                                                     PART I
                                                                     ITEM 1
                                                                     PAGE 7
                               BIOPURE CORPORATION

              Notes to Condensed Consolidated Financial Statements
                                  July 29, 2000
                                   (Unaudited)
                                   (Continued)


     Because the options and warrants are assumed to be earned over the vesting
     period, the final value of the options and warrants (i.e. the compensation
     expense), will not be determined until the vesting is complete. Therefore,
     at each time interval (i.e. quarterly), the options and warrants must be
     marked to fair value (based on a valuation model such as the Black Scholes
     option pricing model). Compensation expense based on fair value will
     continue to be amortized to general and administrative expense on a
     straight-line basis over the vesting period. However, the amount charged to
     expense will be increased or decreased at each point in time based on the
     then current fair value of the Company's stock.

     Therefore, during each time interval the Company will be required to record
     two amounts, the first, the current period compensation charge, and the
     second, a cumulative catch-up adjustment for the period based on the fair
     value of the options at the end of that period.

6. 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. On February 23, 2000, the United States
     District Court for the District of Massachusetts reaffirmed entry of final
     judgment in favor of Biopure and found on the jurisdiction issue that there
     is no reason to delay the appeal. The plaintiff has filed an appeal of this
     decision. 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 financial statements. At July 29, 2000, the Company had
     $3,508,000 in escrow in connection with this settlement and included this
     amount in current portion of restricted cash. 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 29, 2000

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 as
amended (Form S-1, Registration No. 333-30382). 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 as amended (Form S-1, Registration No. 333-30382) 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 29, 2000 COMPARED TO THREE MONTHS ENDED JULY 31, 1999

Total revenues increased 30.4 % to $836,000 in the third quarter of fiscal 2000
from $641,000 in the third quarter of fiscal 1999. The increase in revenues is
due to an increase in the number of units sold.

Cost of revenues decreased 30.2% to $1,215,000 in the third quarter of fiscal
2000 from $1,741,000 in the third quarter of fiscal 1999. This decline is due to
improved production yields and increased production volumes, lowering the cost
per unit of product.

Research and development expenses decreased 16.4% to $6,229,000 in the third
quarter of fiscal 2000 from $7,449,000 in the third quarter of fiscal 1999. This
decrease was primarily due to the expenses associated with the pivotal Phase III
clinical trial activities for Hemopure.

Sales and marketing expenses decreased 14.8% to $617,000 in the third quarter of
fiscal 2000 from $724,000 in the third quarter of fiscal 1999. This decrease was
primarily attributable to a reduction in sales promotion and advertising
expenses for Oxyglobin versus the same period last year.

General and administrative expenses increased 32.0% to $1,529,000 in the third
quarter of fiscal 2000 from $1,158,000 in the third quarter of fiscal 1999. This
increase is primarily due to an expansion of business development, marketing and
medical education activities for Hemopure.

Other income was $1,563,000 in the third quarter of fiscal 2000 compared to
$88,000 in the third quarter of fiscal 1999. Net proceeds from our follow-on
offering of 2,565,000 shares of Class A Common Stock, in March 2000, were
$83,775,000. As a result of the increase in cash, we earned $1,580,000 in
interest during the third quarter of fiscal 2000, versus $202,000 during the
third quarter of fiscal 1999.

<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 29, 2000
                                   (Continued)


Basic net loss per common share for the current quarter was $0.29, compared with
a basic net loss per common share of $2.29 and a pro forma basic net loss per
common share of $1.38 for the same period in 1999. For the three months ended
July 31, 1999, the basic and the pro forma net loss per common share include a
one-time charge of $1.45 and $0.87, respectively, related to $17,915,000 million
in common stock dividends issued to preferred stockholders at the time of our
initial public offering (August 1999). All per share amounts for 1999 have been
reported pro forma to reflect the increased amount of common stock outstanding
resulting from preferred stock conversions at the time of the initial public
offering in 1999.

NINE MONTHS ENDED JULY 29, 2000 COMPARED TO NINE MONTHS ENDED JULY 31, 1999

Total revenues decreased 2.0% to $2,143,000 in the first nine months of fiscal
2000 from $2,186,000 in the first nine months of fiscal 1999. The first nine
months of fiscal 1999 included the national launch of Oxyglobin and sales
promotions that were not repeated in the first nine months of fiscal 2000.
Revenues in the first nine months of fiscal 2000 consisted primarily of
Oxyglobin (veterinary product) sales.

Cost of revenues decreased 29.5% to $3,506,000 in the first nine months of
fiscal 2000 from $4,970,000 in the first nine months of fiscal 1999. This
decline is due to improved production yields and lower manufacturing spending,
lowering the cost per unit of product.

Research and development expenses increased 30.7% to $22,631,000 in the first
nine months of fiscal 2000 from $17,320,000 in the first nine months of fiscal
1999. This increase was primarily due to the expenses associated with the
pivotal Phase III clinical trial activities for Hemopure.

Sales and marketing expenses decreased 21.1% to $1,765,000 in the first nine
months of fiscal 2000 from $2,236,000 in the first nine months of fiscal 1999.
This decrease was primarily attributable to expenses of normal operations in the
first nine months of fiscal 2000 versus expenses associated with the national
launch of Oxyglobin and related sales promotions in the first nine months of
1999.

General and administrative expenses increased 78.5% to $6,377,000 in the first
nine months of fiscal 2000 from $3,572,000 in the first nine months of fiscal
1999. The increase is primarily due to non-cash compensation expense for stock
options and warrants issued to certain consultants and directors in August and
November 1999. We are required to account for the fair market value of these
options and warrants, per FAS 123, amortized over the vesting period, and
revalued each quarter based on the closing stock price. For the first nine
months of fiscal 2000, we charged $1,786,000 to compensation expense versus no
comparable charge for the same period last year. The remainder of the increase
is primarily due to an expansion of business development, marketing and medical
education activities for Hemopure.

Other income was $2,854,000 in the first nine months of fiscal 2000 compared to
$347,000 in the first nine months of fiscal 1999. As a result of the increase in
cash from a public offering of common stock in March 2000, we earned $2,904,000
in interest during the first nine months of fiscal 2000, versus $564,000 during
the first nine months of fiscal 1999.

<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 29, 2000
                                   (Continued)


Basic net loss per common share for the first nine months of fiscal 2000 was
$1.24, compared with a basic net loss per common share of $3.53 and a pro forma
basic net loss per common share of $2.21 for the same period in 1999. For the
nine months ended July 31, 1999, the basic and the pro forma net loss per common
share include a one-time charge of $1.45 and $0.91, respectively, related to
$17,915,000 in common stock dividends issued to preferred stockholders at the
time of our initial public offering (August 1999). All per share amounts for
1999 have been reported pro forma to reflect the increased amount of common
stock outstanding resulting from preferred stock conversions at the time of the
initial public offering.

LIQUIDITY AND CAPITAL RESOURCES

At July 29, 2000, we had current assets of $103,149,000, consisting primarily of
$95,616,000 in cash and cash equivalents and $3,089,000 in net inventory. Cash
included the net proceeds of $83,775,000 from a public offering of common stock
in March 2000. At July 29, 2000, current liabilities were $12,717,000.

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

Our primary investment objective is preservation of principal, and we currently
invest in high-grade commercial paper.

We have not been profitable since inception and had an accumulated deficit of
$279,633,000 as of July 29, 2000. We will continue to generate losses from
operations for the foreseeable future.

We believe our current cash, cash equivalents and short-term investments will be
sufficient to meet our projected operating requirements through fiscal 2001. Our
cash requirements may vary significantly from current projections.

As of October 31, 1999, we had net operating loss carryforwards of approximately
$161,000,000 to offset future federal and state taxable income through 2019. 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, 1999. Utilization of such losses in future years may be limited under the
change of stock ownership rules of the Internal Revenue Service.

YEAR 2000 COMPUTER SYSTEMS COMPLIANCE

All of our computer hardware and software has been upgraded for Year 2000
compliance. All of our key vendors have provided assurance that they are Year
2000 compliant. While there were no Year 2000 related problems at the transition
in the Year 2000, we are maintaining our contingency plans in the event any
problems arise in the future.


<PAGE>   13

                                                                     FORM 10-Q
                                                                     PART 1
                                                                     ITEM 3
                                                                     PAGE 11

                               BIOPURE CORPORATION

                     Management's Discussion and Analysis of
                  Financial Condition and Results of Operations
                                  July 29, 2000
                                   (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. These investments are subject to the risk of a decline in
interest rates.

<PAGE>   14

                                                                     FORM 10-Q
                                                                     PART II
                                                                     ITEM 1-6
                                                                     PAGE 12

                               BIOPURE CORPORATION
                           Part II - Other Information
                                  July 29, 2000


ITEM 1 - LEGAL PROCEEDINGS

Reference is made to Item 103 in the Corporation's Annual Report on Form 10-K.
On February 23, 2000, the Court reaffirmed entry of final judgment in favor of
Biopure and found that there is no reason to delay the plaintiff's appeal. The
plaintiff has filed an appeal of this decision.

ITEM 2 - CHANGES IN SECURITIES AND USE OF PROCEEDS

Warrants to purchase 3,148 shares of Class A Common Stock were exercised in the
third quarter of fiscal 2000 for aggregate proceeds to the Corporation of
$37,776. The Corporation relied on Section 4(2) of the Securities Act of 1933
and Regulation D under the Securities Act of 1933 in issuing shares upon the
exercise of warrants.


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>   15

                                                                     FORM 10-Q
                                                                     PART II
                                                                     PAGE 13

                                   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 12, 2000             By: /s/ Carl W. Rausch
                                              ------------------------
                                              CARL W. RAUSCH
                                              Chairman of the Board
                                              Chief Executive Officer


     Date:  September 12, 2000             By: /s/ Francis H. Murphy
                                              ------------------------
                                              FRANCIS H. MURPHY
                                              Chief Financial Officer

<PAGE>   16

                                  EXHIBIT INDEX


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

27.1        Financial Data Schedule for the nine months ended
            July 29, 2000

27.2        Financial Data Schedule for the three months ended
            July 29, 2000