The gemara launches into a major discussion about the concept of כל מילתא דאמר רחמנא לא תעביד, אי עביד לא מהני. Meaning, when the Torah says not to do something, is there a built in mechanism that makes it ineffective even if it is done (rava), or is it effective. The gemara explains that according to Abbaye it must be effective because otherwise there was nothing violated for which to receive malkus, but according to Rava the malkus is for performing the action that the Torah said not to, but it will not be effective.
R. Akiva Eiger (Comments to Y.D. 10:1) explains that the application of this concept is only in cases where by the Torah saying it doesn't work, the Torah is accomplishing something. Meaning, there is a preventative clause built in to any aveira that if the issur can be reduced by it not going into effect, the Torah doesn't enable the issur to go into effect. For example, if one were to shecht on shabbos, the concept of אי עביד לא מהני would not apply to invalidate the shechita because even if the shechita were invalidated, it would in no way reduce the violation of shabbos. We can only apply this concept to a places where by invalidating the effect, it would lessen the violation such as divorcing a woman who one raped. The Torah doesn't want her to be divorced so by invalidating the divorce, the violation is lessened (but the gemara learns from a pasuk that the this is an exception to the rule and the divorce is binding).
Therefore, R. Akiva Eiger asks that if one would shecht an animal with a knife that is forbidden to benefit from because it is avoda zarah, it would make sense to apply אי עביד לא מהני to invalidate the shechita. The benefit from the knive is dependent on the shechita being valid, therefore invalidating the shechita would prevent the violation of benefiting from the knife. R. Akiva Eiger points out based on the Turei Even in Rosh Hashana that even Abbaye who holds אי עביד מהני would only say that in a situation where even if we undermine the effect of the issur, it doesn't negate the fact that he violated the din of the torah. In other words, since even after we undermine the effect of the issur, he nonetheless violated the מימרא דרחמנא (for which rava says he gets malkus), there is no point in negating the effect of his actions since it doesn't truly rectify the violation. However, in a case where undermining the effect will completely undermine the violation, even Abbaye would agree that we apply the concept of אי עביד לא מהני. Therefore, when one shechts with a knife that they are forbidden to derive benefit from, by invalidating the shechita and rendering the animal a ne'veila, we are completely circumventing the violation becasue the violation is not to do an action, it is to benefit. By rendering the animal a neveila it comes out that he never even violated the מימרא דרחמנא so even Abbaye should agree that the animal is considered a ne'veila. R. Akiva Eiger leaves with at צריך עיון.