<PAGE>   1
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                       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           January 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 February 25, 2000 was:

            Class A Common Stock, $.01 par value.................22,345,876
            Class B Common Stock, $1.00 par value.....................117.7

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<PAGE>   2


                               BIOPURE CORPORATION

                               INDEX TO FORM 10-Q



                                                                            Page
                                                                            ----


Part I - Financial Information:

    Item 1 - Financial Statements (Unaudited)

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

           Condensed Consolidated Statements of
           Operations for the quarters ended
           January 29, 2000 and January 30, 1999                               2

           Condensed Consolidated Statements of Cash
           Flows for the three months ended
           January 29, 2000 and January 30, 1999                               3

           Notes to Condensed Consolidated
           Financial Statements                                              4-7


    Item 2 - Management's Discussion and Analysis
             of Financial Condition and Results of Operations                8-9

    Item 3 - Quantitative and Qualitative Disclosure of Market Risk           10


Part II - Other Information:

    Item 1 - Legal Proceedings                                                11

    Item 2 - Changes in Securities and Use of Proceeds                        11

    Item 6 - Exhibits and Reports on Form 8-K                                 11

Signatures                                                                    12

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>

                                                        January 29, 2000         October 31, 1999
                                                        ----------------         ----------------
<S>                                                        <C>                      <C>
Assets:
Current assets:
    Cash and cash equivalents                               $    22,146             $    30,778
    Accounts receivable, net                                        336                     321
    Inventories, net                                              2,564                   3,182
    Current portion of restricted cash                            3,508                   3,508
    Other current assets                                            459                     488
                                                            -----------             -----------
         Total current assets                                    29,013                  38,277

Property, plant and equipment, net                               26,502                  27,447
Investment in affiliate                                             101                     101
Other assets                                                        418                     405
                                                            -----------             -----------
         Total assets                                       $    56,034             $    66,230
                                                            ===========             ===========

Liabilities and stockholders' equity:
Current liabilities:
    Accounts payable                                        $       446               $     741
    Accrued expenses                                             10,309                   9,664
                                                            -----------             -----------
    Total current liabilities                                    10,755                  10,405

Deferred compensation                                             1,805                   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, 22,288,706 shares
      outstanding at January 29, 2000 and 22,280,867
      at October 31, 1999                                           223                     223
     Class B, $1.00 par value, 179 shares
      authorized, 117.7 shares outstanding                            -                       -
    Capital in excess of par value                              283,720                 282,054
    Contributed capital                                          24,574                  24,574
    Notes receivable                                             (2,509)                 (2,463)
    Accumulated deficit                                        (262,534)               (250,351)
                                                            ------------             -----------

Total stockholders' equity                                       43,474                  54,037
                                                            ------------             -----------

        Total liabilities and stockholders'
         equity                                             $    56,034             $    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
                                              -------------------------------------
                                              January 29, 2000     January 30, 1999
                                              ----------------     ----------------

<S>                                               <C>                  <C>
Revenues:
         Oxyglobin                                $    595             $     671
         Other                                           3                    62
                                                  --------             ---------
              Total revenues                           598                   733
Cost of revenues                                     1,189                 1,680
                                                  --------             ---------
Gross profit (loss)                                   (591)                 (947)

Operating expenses:
         Research and development                    8,259                 4,283
         Sales and marketing                           579                   729
         General and administrative                  3,112                 1,092
                                                  --------             ---------
         Total operating expenses                   11,950                 6,104
                                                  --------             ---------

Loss from operations                               (12,541)               (7,051)
Other income                                           358                   207
                                                  --------             ---------

Net loss applicable to
common stockholders                               $(12,183)              $(6,844)
                                                  =========            =========

Historical:
         Basic net loss
         per common share                         $  (0.55)            $   (0.55)

         Weighted average shares used in
         computing basic net loss
         per common share                           22,282                12,422

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

         Weighted average shares used in
         computing pro forma basic net
         loss per common share                                            18,948
</TABLE>


                             See accompanying notes.






<PAGE>   5


                                                                       FORM 10-Q
                                                                          PART I
                                                                          ITEM 1
                                                                          PAGE 3

                               BIOPURE CORPORATION

                 Condensed Consolidated Statement of Cash Flows
                                 (In thousands)
                                   (Unaudited)
<TABLE>
<CAPTION>

                                                                         Three Months Ended
                                                              ----------------------------------------
                                                              January 29, 2000       January 30, 1999
                                                              ----------------       ----------------

<S>                                                               <C>                        <C>
Operating activities:
    Net loss                                                     $ (12,183)                 $ (6,844)

Adjustments to reconcile net loss to net
 cash used in operating activities:
    Depreciation                                                       998                       984
    Equity compensation                                              1,688                         -
    Deferred compensation                                               17                        69
    Accrued interest on stockholders' notes receivable                 (46)                      (46)
    Accounts receivable                                                (15)                      (16)
    Inventories                                                        618                      (146)
    Other current assets                                                29                       (64)
    Accounts payable                                                  (295)                     (707)
    Accrued expenses                                                   645                      (237)
                                                                 ----------                 ---------
      Net cash used in operating activities                         (8,544)                   (7,007)


Investing activities:
    Purchase of property, plant and equipment                          (53)                     (622)
    Other assets                                                       (13)                      (16)
                                                                 ----------                 ---------
      Net cash used in investing activities                            (66)                     (638)

Financing activities:
    Net proceeds from sale of common stock                             (30)                        -
    Net proceeds from sale of preferred stock                            -                    16,946
    Payment of long-term debt                                            -                      (500)
    Proceeds from exercise of options                                    8                        28
                                                                 ----------                 ---------
      Net cash provided by (used in) financing activities              (22)                   16,474
                                                                 ----------                 ---------

Net increase (decrease) in cash and cash equivalents                (8,632)                    8,829
Cash and cash equivalents at beginning of period                    30,778                     6,063
                                                                 ----------                 ---------
Cash and cash equivalents at end of period                       $  22,146                  $ 14,892
                                                                 ==========                 =========
</TABLE>





                             See accompanying notes.




<PAGE>   6

                                                                       FORM 10-Q
                                                                          PART I
                                                                          ITEM 1
                                                                          PAGE 4

                               BIOPURE CORPORATION

              Notes to Condensed Consolidated Financial Statements
                                January 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 month period ended
         January 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
                                January 29, 2000
                                   (Unaudited)
                                   (Continued)


         The following table sets forth the computation of basic and pro forma
         loss per share for the three months ended January 29, 2000 and January
         30, 1999 (in thousands, except per share data):
<TABLE>
<CAPTION>

                                                                                          Three Months Ended
                                                                                 -------------------------------------
                                                                                 January 29, 2000     January 30, 1999
                                                                                 ----------------     ----------------

          <S>                                                                      <C>                  <C>
           Historical:
            Net loss applicable
            to common stockholders                                                   $(12,183)            $  (6,844)
                                                                                     =========            ==========


            Weighted-average number of
            common shares outstanding                                                  22,282                12,422
                                                                                     =========            ==========
          Basic net loss
          per common share                                                           $  (0.55)            $   (0.55)
                                                                                     =========            ==========

           Pro forma:
            Weighted-average number of
            common shares:
                Historical outstanding                                                                       12,422
                Issued upon conversion
                of preferred stock                                                                            6,526
                                                                                                          ---------
                Total weighted-average number
                of common shares used in
                computing pro forma basic net
                loss per common share                                                                        18,948
                                                                                                          ==========

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









<PAGE>   8
                                                                       FORM 10-Q
                                                                          PART I
                                                                          ITEM 1
                                                                          PAGE 6

                               BIOPURE CORPORATION

              Notes to Condensed Consolidated Financial Statements
                                January 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:

<TABLE>
<CAPTION>

                                                            January 29, 2000            October 31, 1999
                                                            ----------------            ----------------
         In thousands
        <S>                                                     <C>                        <C>
         Raw materials .....................................    $    719                   $    690
         Work-in-process ...................................         110                        134
         Finished goods ....................................       1,735                      2,358
                                                                --------                   --------
                                                                $  2,564                   $  3,182
                                                                ========                   ========
</TABLE>

4.  ACCRUED EXPENSES

           Accrued expenses consisted of the following:
<TABLE>
<CAPTION>

                                                            January 29, 2000            October 31, 1999
                                                            ----------------            ----------------

           In thousands
          <S>                                                 <C>                         <C>
           Settlement ......................................    $  3,508                   $  3,508
           Phase III clinical trial ........................       4,655                      2,925
           Initial public offering .........................           -                        619
           Other ...........................................       2,146                      2,612
                                                                --------                   --------
                                                                $ 10,309                   $  9,664
                                                                ========                   ========
</TABLE>


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, $1,700,000 was charged
           to non-cash compensation expense for the quarter ended January 29,
           2000.





<PAGE>   9
                                                                       FORM 10-Q
                                                                          PART I
                                                                          ITEM 1
                                                                          PAGE 7

                               BIOPURE CORPORATION

              Notes to Condensed Consolidated Financial Statements
                                January 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. 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 January 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
                                January 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 JANUARY 29, 2000 COMPARED TO THREE MONTHS ENDED JANUARY 30,
1999

Total revenues decreased 18.4% to $598,000 in the first quarter of fiscal 2000
from $733,000 in the first quarter of fiscal 1999. The first quarter of fiscal
1999 was the national launch period for Oxyglobin. Revenues in the first quarter
of fiscal 2000 consisted primarily of Oxyglobin (veterinary product) sales.

Cost of revenues decreased 29.2% to $1,189,000 in the first quarter of fiscal
2000 from $1,680,000 in the first quarter of fiscal 1999. This decline is due to
a 20% reduction in unit sales volume and a reduction in manufacturing spending.

Research and development expenses increased 92.8% to $8,259,000 in the first
quarter of fiscal 2000 from $4,283,000 in the first 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 20.6% to $579,000 in the first quarter of
fiscal 2000 from $729,000 in the first quarter of fiscal 1999. This decrease was
primarily attributable to expenses of normal operations in the first quarter of
fiscal 2000 compared to the national launch expenses for the same period last
year. Selling, marketing and distribution expenses and headcount have also been
reduced versus the same period last year.

General & administrative expenses increased 185.0% to $3,112,000 in the first
quarter of fiscal 2000 from $1,092,000 in the first quarter 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 quarter of fiscal 2000,
we charged $1,700,000 to compensation expense versus no compensation expense for
the same period last year.

Total other income was $358,000 in the first quarter of fiscal 2000 compared to
$207,000 in the first quarter of fiscal 1999. This favorable change of $151,000
was primarily associated with a $201,000 increase in interest income.



<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
                                January 29, 2000
                                   (Continued)



Basic net loss per common share for the current quarter was $0.55, compared with
a basic net loss per common share of $0.55 and a pro forma basic net loss per
common share of $0.36 for the same period in 1999.


LIQUIDITY AND CAPITAL RESOURCES

At January 29, 2000, we had current assets of $29,013,000, which consisted
primarily of $22,146,000 in cash and cash equivalents and $2,564,000 in net
inventory. At January 29, 2000, current liabilities were $10,755,000.

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

We have not been profitable since inception and had an accumulated deficit of
$262,534,000 as of January 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 more than sufficient to meet our projected requirements through June 2000,
including the anticipated completion of our pivotal Phase III trial. On March
13, 2000, Biopure entered into a firm commitment underwriting agreement to sell
2,500,000 shares of class A common stock at $35.00 per share for estimated net
proceeds of $81,630,000. 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>   12

                                                                       FORM 10-Q
                                                                          PART I
                                                                          ITEM 3
                                                                         PAGE 10

                               BIOPURE CORPORATION

                     Management's Discussion and Analysis of
                  Financial Condition and Results of Operations
                                January 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>   13

                                                                       FORM 10-Q
                                                                         PART II
                                                                        ITEM 1-6
                                                                         PAGE 11

                               BIOPURE CORPORATION
                           Part II - Other Information
                                January 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.

ITEM 2 - CHANGES IN SECURITIES AND USE OF PROCEEDS

Warrants and employee stock options to purchase 7,839 shares of Class A Common
Stock were exercised in the first quarter of fiscal 2000 for aggregate proceeds
to the Corporation of $7,492.50. The Corporation relied on the SEC Rule 701 and
Section 4(2) of the Securities Act of 1933.

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>   14

                                                                       FORM 10-Q
                                                                         PART II
                                                                         PAGE 12

                                   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:  March 14, 2000                      By: /s/ Carl W. Rausch
                                                         -------------------
                                                         Carl W. Rausch
                                                         --------------
                                                         Chairman of the Board
                                                         Chief Executive Officer


           Date:  March 14, 2000                      By: /s/ Francis H. Murphy
                                                         ----------------------
                                                         Francis H. Murphy
                                                         -----------------
                                                         Chief Financial Officer














<PAGE>   15


                                  EXHIBIT INDEX






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

27                                        Financial Data Schedule for three
                                          months ended January 29, 2000