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                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
                            ------------------------

                                 SCHEDULE 13E-3
                                  RULE 13E-100
                   TRANSACTION STATEMENT UNDER SECTION 13(e)
        OF THE SECURITIES EXCHANGE ACT OF 1934 AND RULE 13e-3 THEREUNDER
                               (AMENDMENT NO. 3)
                            ------------------------

                            SWISS ARMY BRANDS, INC.
                              (NAME OF THE ISSUER)

                            SWISS ARMY BRANDS, INC.
                      (NAME OF PERSON(S) FILING STATEMENT)

                    COMMON STOCK, PAR VALUE $0.10 PER SHARE
                         (TITLE OF CLASS OF SECURITIES)

                                   870827102
                     (CUSIP NUMBER OF CLASS OF SECURITIES)

                               THOMAS M. LUPINSKI
                            CHIEF FINANCIAL OFFICER
                            SWISS ARMY BRANDS, INC.
                               ONE RESEARCH DRIVE
                           SHELTON, CONNECTICUT 06484
                           TELEPHONE: (203) 929-6391
          (NAME, ADDRESS AND TELEPHONE NUMBER OF PERSONS AUTHORIZED TO
  RECEIVE NOTICES AND COMMUNICATIONS ON BEHALF OF PERSON(S) FILING STATEMENT)
                            ------------------------

                                WITH COPIES TO:
                           PRISCILLA C. HUGHES, ESQ.
                            MORRISON & FOERSTER LLP
                          1290 AVENUE OF THE AMERICAS
                            NEW YORK, NY 10104-0050
                           TELEPHONE: (212) 468-8000

     This statement is filed in connection with (check the appropriate box):

     a.  [ ] The filing of solicitation materials or an information statement
subject to Regulation 14A, Regulation 14C or Rule 13e-(c) under the Securities
Exchange Act of 1934.

     b.  [ ] The filing of a registration statement under the Securities Act of
1933.

     c.  [X] A tender offer.

     d.  [ ] None of the above.

     Check the following box if the soliciting materials or information
statement referred to in checking box (a) are preliminary copies:  [ ]

     Check the following box if the filing is a final amendment reporting the
results of the transaction:  [ ]
                            ------------------------

                           CALCULATION OF FILING FEE

<Table>
<Caption>
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                TRANSACTION VALUATION*                                  AMOUNT OF FILING FEE
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                     $32,095,854                                             $2,952.82
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</Table>

*  Estimated for purposes of calculating the filing fee. Calculated by
   multiplying $9.00, the per share tender offer price, by 3,566,206, the sum of
   (i) 2,666,706 currently outstanding shares of common stock of Swiss Army
   Brands, Inc. and (ii) outstanding options with an exercise price of less than
   $9.00 with respect to 899,500 shares of common stock. The amount of the
   filing fee, calculated in accordance with Rule 0-11 of the Securities
   Exchange Act of 1934, as amended.

[X] Check box if any part of the fee is offset as provided by Rule 0-11(a)(2)
    and identify the filing with which the offsetting fee was previously paid.
    Identify the previous filing by registration statement number, or the form
    or schedule and the date of its filing.

<Table>
                                                                 
AMOUNT PREVIOUSLY PAID:      $2,952.82                   FILING PARTY:    SABI ACQUISITION CORP.
FORM OR REGISTRATION NO.:    SCHEDULE TO/13E-3           DATE FILED:      AUGUST 13, 2002
</Table>

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                                  INTRODUCTION

     This Amendment No. 3 amends and supplements the Schedule 13E-3 dated July
23, 2002 (as amended and supplemented, the "Schedule 13E-3") relating to the
offer by SABI Acquisition Corp. ("Purchaser"), a Delaware corporation which is
wholly owned by Victorinox AG ("Victorinox"), as set forth in the Tender Offer
Statement on Schedule TO, dated July 23, 2002, (as amended and supplemented, the
"Schedule TO"), to purchase all of the outstanding shares of common stock of
Swiss Army Brands, Inc., a Delaware corporation (the "Company" or "SABI"), par
value $.10 per share, at a price of $9.00 per share, net to the seller in cash,
less any required withholding of taxes and without any payment of interest, upon
the terms and subject to the conditions set forth in the Offer to Purchase dated
July 23, 2002 (the "Offer to Purchase"), a copy of which was previously filed as
Exhibit (a)(1)(A) hereto, and in the related Letter of Transmittal (the "Letter
of Transmittal"), a copy of which was previously filed as Exhibit (a)(1)(B)
hereto (which, together with the Offer to Purchase, as amended or further
supplemented from time to time, constitute the "Offer"). The Schedule TO was
originally filed by Purchaser and Victorinox with the Securities and Exchange
Commission (the "SEC") on July 23, 2002 and amended on July 29, 2002, August 13,
2002 and August 20, 2002.

     In response to the Offer, the Company filed a Solicitation/Recommendation
Statement on Schedule 14D-9 on July 23, 2002 and amended the Schedule 14D-9 on
July 29, 2002, August 13, 2002, August 20, 2002 and August 23, 2002 (The
Schedule 14D-9). The information contained in the Schedule 14D-9 is expressly
incorporated by reference in response to the items of this Schedule 13E-3.

     Capitalized terms used but not defined herein shall have the meanings
ascribed to them in the Offer to Purchase and the Schedule TO.

ITEM 16.  EXHIBITS

     Item 16 is hereby amended and supplemented to refile the revised exhibit
c(2):

<Table>
         
(c)(2)      Project Alps Materials for Discussion presented by Needham &
            Company, Inc. to the Special Committee of the Board of
            Directors of the Company on June 11, 2002.+
</Table>

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+ Portions of this exhibit have been omitted pursuant to a request for
  confidential treatment and have been separately filed with the SEC.


                                   SIGNATURES

     After due inquiry and to the best of my knowledge and belief, I certify
that the information set forth in this Statement is true, complete and correct.

                                          SWISS ARMY BRANDS, INC.

                                          By:    /s/ THOMAS M. LUPINSKI
                                            ------------------------------------
                                          Name:  Thomas M. Lupinski
                                          Title: Senior Vice President, Chief
                                                 Financial Officer, Secretary
                                                 and Treasurer

Dated:  August 23, 2002


                                 EXHIBIT INDEX

<Table>
        
(c)(2)     Project Alps Materials for Discussion presented by Needham &
           Company, Inc. to the Special Committee of the Board of
           Directors of the Company on June 11, 2002.+
</Table>

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+ Portions of this exhibit have been omitted pursuant to a request for
  confidential treatment and have been separately filed with the SEC.