The derby match was abandoned after 57 minutes on April 19 after an object was thrown at Besiktas's 65-year-old head coach Senol Gunes from the home end.
Gunes was rushed to hospital and required stitches to cover up his head wound.
With 32 minutes of the match still to play, the Turkish Football Federation ordered the remainder of the semi-final to be replayed on May 3 behind closed doors – but Besiktas have now declared that they don't want any involvement.
"We have been on the field for 115 years; we have won, had draws or lost on the field. In order not to accept losing to backstage football politics, we will not show up," Besiktas said in an official club statement.
The Istanbul club were down to 10 men in the second leg, following a 2-2 draw in the first, after former Real Madrid defender Pepe was sent off. That would have meant the Super Lig champions playing a man down in the rescheduled, downsized fixture.
The Turkish Football Federation are yet to respond.
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