<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                 APRIL 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 May 26, 2000 was:

         Class A Common Stock, $.01 par value............... 24,930,217
         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
           April 29, 2000 and October 31, 1999                               1

           Condensed Consolidated Statements of Operations for the
           quarters ended April 29, 2000 and May 1, 1999 and
           for the six months ended April 29, 2000 and May 1, 1999           2

           Condensed Consolidated Statements of Cash Flows
           for the six months ended April 29, 2000 and May 1, 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 4 -   Submission of Matters to a Vote of Security Holders          12

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

Signatures                                                                  13

Exhibit Index





<PAGE>   3
                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 1
                                                                       PAGE 1

                               BIOPURE CORPORATION

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

<TABLE>
<CAPTION>
Assets:                                                          APRIL 29, 2000     OCTOBER 31, 1999
                                                                 --------------     ----------------
<S>                                                                <C>                 <C>
Current assets:
    Cash and cash equivalents                                      $ 100,848           $  30,778
    Accounts receivable, net                                             439                 321
    Inventories, net                                                   2,588               3,182
    Current portion of restricted cash                                 3,508               3,508
    Other current assets                                                 711                 488
                                                                   ---------           ---------
         Total current assets                                        108,094              38,277

Property, plant and equipment, net                                    25,620              27,447
Investment in affiliate                                                  101                 101
Other assets                                                             441                 405
                                                                   ---------           ---------
         Total assets                                              $ 134,256           $  66,230
                                                                   =========           =========

Liabilities and stockholders' equity:
Current liabilities:
    Accounts payable                                               $     975           $     741
    Accrued expenses                                                  10,971               9,664
                                                                   ---------           ---------
    Total current liabilities                                         11,946              10,405

Deferred compensation                                                  1,751               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, 24,930,217 shares
        outstanding at April 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                                   370,172             282,054
    Contributed capital                                               24,574              24,574
    Notes receivable                                                  (1,994)             (2,463)
    Accumulated deficit                                             (272,442)           (250,351)
                                                                   ---------           ---------

Total stockholders' equity                                           120,559              54,037
                                                                   ---------           ---------
         Total liabilities and stockholders'
         equity                                                    $ 134,256           $  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                     SIX MONTHS ENDED
                                                  ---------------------------           ---------------------------
                                                  APRIL 29,           MAY 1,            APRIL 29,            MAY 1,
                                                  ---------          --------           ---------          --------
                                                    2000               1999               2000               1999
                                                  --------           --------           --------           --------

<S>                                               <C>                <C>                <C>                <C>
Revenues:
         Oxyglobin                                $    710           $    810           $  1,304           $  1,481
         Other                                          --                  2                  3                 64
                                                  --------           --------           --------           --------
                Total revenues                         710                812              1,307              1,545
Cost of revenues                                     1,102              1,549              2,291              3,229
                                                  --------           --------           --------           --------
Gross profit (loss)                                   (392)              (737)              (984)            (1,684)

Operating expenses:
         Research and development                    8,143              5,588             16,402              9,871
         Sales and marketing                           569                783              1,148              1,512
         General and administrative                  1,736              1,322              4,848              2,414
                                                  --------           --------           --------           --------
         Total operating expenses                   10,448              7,693             22,398             13,797
                                                  --------           --------           --------           --------

Loss from operations                               (10,840)            (8,430)           (23,382)           (15,481)
Other income                                           933                 52              1,291                259
                                                  --------           --------           --------           --------

Net loss                                          $ (9,907)          $ (8,378)          $(22,091)          $(15,222)
                                                  ========           ========           ========           ========

Historical:
         Basic net loss
         per common share                         $  (0.42)          $  (0.67)          $  (0.96)          $  (1.23)

         Weighted average shares used in
         computing basic net loss
         per common share*                          23,580             12,422             22,938             12,333

Pro forma:
         Pro forma basic net loss
         per common share                                            $  (0.42)                             $  (0.79)

         Weighted average shares used in
         computing pro forma basic net
         loss per common share                                         19,741                                19,250
</TABLE>


                             See accompanying notes.

         *Actual shares outstanding at April 29, 2000 were 24,930.






<PAGE>   5


                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 1
                                                                       PAGE 3

                               BIOPURE CORPORATION

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

<TABLE>
<CAPTION>
                                                                        SIX MONTHS ENDED
                                                                --------------------------------
                                                                APRIL 29, 2000       MAY 1, 1999
                                                                --------------       -----------

<S>                                                               <C>                 <C>
Operating activities:
    Net loss                                                      $ (22,091)          $ (15,222)

Adjustments to reconcile net loss to net
  cash used in operating activities:
    Depreciation                                                      2,049               1,937
    Equity compensation                                               1,820                  42
    Deferred compensation                                               (37)                  2
    Accrued interest on stockholders' notes receivable                  (86)                (91)
    Accounts receivable                                                (118)               (259)
    Inventories                                                         594              (1,493)
    Other current assets                                               (223)                (50)
    Accounts payable                                                    234                (971)
    Accrued expenses                                                  1,307               1,223
                                                                  ---------           ---------
       Net cash used in operating activities                        (16,551)            (14,882)

Investing activities:
    Purchase of property, plant and equipment                          (222)             (1,361)
    Other assets                                                        (36)                 81
                                                                  ---------           ---------
       Net cash used in investing activities                           (258)             (1,280)

Financing activities:
    Net proceeds from sale of common stock                           83,739                  --
    Net proceeds from sale of preferred stock                            --              25,552
    Payment of long-term debt                                            --              (1,000)
    Repurchase of common stock                                           --              (1,000)
    Payment of notes receivable from shareholders                       556                  --
    Proceeds from exercise of options and warrants                      472                  88
    Proceeds from exercise of non lapse restricted stock              2,112                  --
                                                                  ---------           ---------
       Net cash provided by financing activities                     86,879              23,640
                                                                  ---------           ---------

Net increase in cash and cash equivalents                            70,070               7,478
Cash and cash equivalents at beginning of period                     30,778               6,063
                                                                  ---------           ---------
Cash and cash equivalents at end of period                        $ 100,848           $  13,541
                                                                  =========           =========
</TABLE>


                             See accompanying notes.




<PAGE>   6


                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 1
                                                                       PAGE 4

                               BIOPURE CORPORATION

              Notes to Condensed Consolidated Financial Statements
                                 April 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 six months
         periods ended April 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
                                 April 29, 2000
                                   (Unaudited)
                                   (Continued)


The following table sets forth the computation of basic and pro forma loss per
share for the three and six months ended April 29, 2000 and May 1, 1999 (in
thousands, except per share data):

<TABLE>
<CAPTION>
                                       THREE MONTHS ENDED            SIX MONTHS ENDED
                                     ----------------------      ------------------------
                                     APRIL 29,       MAY 1,       APRIL 29,        MAY 1,
                                     ---------     --------      ----------      --------
                                       2000          1999           2000           1999
                                     --------      --------      ----------      --------

<S>                                  <C>           <C>           <C>             <C>
Historical:
  Net loss applicable
  to common stockholders             $ (9,907)     $ (8,378)     $  (22,091)     $(15,222)
                                     ========      ========      ==========      ========


  Weighted-average number of
  common shares outstanding            23,580        12,422          22,938        12,333
                                     ========      ========      ==========      ========

Basic net loss
per common share                     $  (0.42)     $  (0.67)     $    (0.96)     $  (1.23)
                                     ========      ========      ==========      ========

 Pro forma:
  Weighted-average number of
  common shares:
   Historical outstanding                            12,422                        12,333
   Issued upon conversion
   of preferred stock                                 7,319                         6,917
                                                   --------                      --------
   Total weighted-average number
   of common shares used in
   computing pro forma basic net
   loss per common share                             19,741                        19,250
                                                   ========                      ========

 Pro forma basic net loss
 per common share                                  $  (0.42)                     $  (0.79)
                                                   ========                      ========
</TABLE>





<PAGE>   8


                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 1
                                                                       PAGE 6

                               BIOPURE CORPORATION

              Notes to Condensed Consolidated Financial Statements
                                 April 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:

                                              APRIL 29, 2000   OCTOBER 31, 1999
                                              --------------   ----------------
         In thousands
         Raw materials .....................    $     1,030       $     690
         Work-in-process ...................            479             134
         Finished goods ....................          1,079           2,358
                                                -----------       ---------
                                                $     2,588       $   3,182
                                                ===========       =========

4.       ACCRUED EXPENSES

         Accrued expenses consisted of the following:

                                              APRIL 29, 2000   OCTOBER 31, 1999
                                              --------------   ----------------

         In thousands
         Settlement                             $     3,508       $   3,508
         Phase III clinical trial ..........          5,372           2,925
         Public Offerings ..................            493             619
         Other .............................          1,598           2,612
                                                -----------       ---------
                                                $    10,971       $   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, $131,000 and
           $1,820,000 was charged to non-cash compensation expense for the
           quarter ended and the six months ended April 29, 2000, respectively.

<PAGE>   9



                                                                       FORM 10-Q
                                                                       PART I
                                                                       ITEM 1
                                                                       PAGE 7

                               BIOPURE CORPORATION

              Notes to Condensed Consolidated Financial Statements
                                 April 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 relating to the current period
           compensation charge and the second would be 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 April 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
                                 April 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 APRIL 29, 2000 COMPARED TO THREE MONTHS ENDED MAY 1, 1999

Total revenues decreased 12.6% to $710,000 in the second quarter of fiscal 2000
from $812,000 in the second quarter of fiscal 1999. The reduction in revenues is
due to a sales promotion in the second quarter of 1999 that was not repeated in
the second quarter of 2000. Revenues in the second quarter of fiscal 2000
consisted of Oxyglobin (veterinary product) sales.

Cost of revenues decreased 28.9% to $1,102,000 in the second quarter of fiscal
2000 from $1,549,000 in the second quarter of fiscal 1999. This decline is due
to lower unit sales than the second quarter of fiscal 1999 and less
manufacturing spending.

Research and development expenses increased 45.7% to $8,143,000 in the second
quarter of fiscal 2000 from $5,588,000 in the second quarter 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 27.3% to $569,000 in the second quarter
of fiscal 2000 from $783,000 in the second quarter of fiscal 1999. This decrease
was primarily attributable to selling expenses associated with a sales promotion
in the second quarter of 1999 that was not repeated in the second quarter of
fiscal 2000. Marketing and distribution expenses were also lower than the same
period last year.

General & administrative expenses increased 31.3% to $1,736,000 in the second
quarter of fiscal 2000 from $1,322,000 in the second quarter of fiscal 1999. The
increase is partially due to non-cash compensation expense for stock options
issued to certain directors in August 1999. We are required to account for the
fair market value of these options per FAS 123, amortized over the vesting
period, and revalued each quarter based on the closing stock price. For the
second quarter of fiscal 2000, we charged $131,000 to compensation expense
versus no comparable charge for the same period last year. Increased spending in
public and investor relations, salaries and insurance also contributed to the
increase in expenses.

Total other income was $933,000 in the second quarter of fiscal 2000 compared to
$52,000 in the second 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
$83,769,000. As a result of the increase in cash, we earned $950,000 in interest
during the second quarter of fiscal 2000, versus $189,000 during the second
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
                                 April 29, 2000
                                   (Continued)



Basic net loss per common share for the current quarter was $0.42, compared with
a basic net loss per common share of $0.67 and a pro forma basic net loss per
common share of $0.42 for the same period in 1999.

SIX MONTHS ENDED APRIL 29, 2000 COMPARED TO SIX MONTHS ENDED MAY 1, 1999

Total revenues decreased 15.4% to $1,307,000 in the first six months of fiscal
2000 from $1,545,000 in the first six months of fiscal 1999. The first six
months of fiscal 1999 included the national launch of Oxyglobin and sales
promotions that were not repeated in the first six months of fiscal 2000.
Revenues in the first six months of fiscal 2000 consisted primarily of Oxyglobin
(veterinary product) sales.

Cost of revenues decreased 29.1% to $2,291,000 in the first six months of fiscal
2000 from $3,229,000 in the first six months of fiscal 1999. This decline is due
to lower unit sales than the first six months of fiscal 1999 and less
manufacturing spending.

Research and development expenses increased 66.2% to $16,402,000 in the first
six months of fiscal 2000 from $9,871,000 in the first six 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 24.1% to $1,148,000 in the first six
months of fiscal 2000 from $1,512,000 in the first six months of fiscal 1999.
This decrease was primarily attributable to expenses of normal operations in the
first six months of fiscal 2000 versus expenses associated with the national
launch of Oxyglobin and related sales promotions in the first six months of
1999. Selling, marketing and distribution expenses were also lower than the same
period last year.

General & administrative expenses increased 100.8% to $4,848,000 in the first
six months of fiscal 2000 from $2,414,000 in the first six 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 six months
of fiscal 2000, we charged $1,820,000 to compensation expense versus no
comparable charge for the same period last year. Increased spending in public
and investor relations, salaries and insurance also contributed to the increase
in expenses.

Total other income was $1,291,000 in the first six months of fiscal 2000
compared to $259,000 in the first six months of fiscal 1999. As a result of the
increase in cash from the follow-on offering, we earned $1,324,000 in interest
during the first six months of fiscal 2000, versus $362,000 during the first six
months of fiscal 1999.

Basic net loss per common share for the first six months of fiscal 2000 was
$0.96, compared with a basic net loss per common share of $1.23 and a pro forma
basic net loss per common share of $0.79 for the same period in 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
                                 April 29, 2000
                                   (Continued)




LIQUIDITY AND CAPITAL RESOURCES

At April 29, 2000, we had current assets of $108,094,000, consisting primarily
of $100,848,000 in cash and cash equivalents and $2,588,000 in net inventory.
Cash included the net proceeds of $83,769,000 from our follow-on offering. At
April 29, 2000, current liabilities were $11,946,000.

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
$272,442,000 as of April 29, 2000. 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 sufficient to meet our projected operating requirements through fiscal 2001,
including the anticipated completion of our pivotal Phase III trial. 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 I
                                                                       ITEM 3
                                                                       PAGE 11

                               BIOPURE CORPORATION

                     Management's Discussion and Analysis of
                  Financial Condition and Results of Operations
                                 April 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.


<PAGE>   14


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

                               BIOPURE CORPORATION
                           Part II - Other Information
                                 April 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 47,814 shares of Class A Common Stock and options to
purchase 16,666 shares of Class A Common Stock were exercised in the second
quarter of fiscal 2000 for aggregate proceeds to the Corporation of $220,138.40.
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. The Corporation relied on the SEC Rule 701 and Section
4(2) of the Securities Act of 1933 in issuing shares upon the exercise of
options.

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

          (a)  The Corporation held its 2000 Annual Meeting on April 5, 2000.

          (b)  Paul A. Looney and C. Everett Koop, M.D. were elected as
               directors at the meeting. The other directors whose terms of
               office continued after the meeting are Daniel P. Harrington,
               David N. Judelson, Stephen A. Kaplan, Carl W. Rausch and Charles
               A. Sanders, M.D.

          (c)  The election of directors was the only matter voted upon at the
               meeting. The shares voted were:

                                                      FOR            WITHHELD

                   C. Everett Koop, M.D.           18,009,810        263,484
                   Paul A. Looney                  18,215,098         58,196

There were no broker held nonvoted shares represented at the meeting.


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:  June 13, 2000                       By: /s/ Carl W. Rausch
                                                         -------------------
                                                         CARL W. RAUSCH
                                                         Chairman of the Board
                                                         Chief Executive Officer


           Date:  June 13, 2000                       By: /s/ Francis H. Murphy
                                                         ----------------------
                                                         FRANCIS H. MURPHY
                                                         Chief Financial Officer



<PAGE>   16







                                  EXHIBIT INDEX






NUMBER     DESCRIPTION

10.28      Underwriting Agreement dated March 13, 2000

27.1       Financial Data Schedule for the six months ended April 29, 2000

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