The only case that the gemara is able to find where one can slaughter the stolen animal on shabbos and pay 4 or 5 is when the thief himself doesn't do the shechita, rather his agent does it for him. Because had the thief done it himself we would say "kim lei b'draba minei" and would not be chayev to pay. The gemara questions how we can have a situation where the shliach does an aviera, and the sender who is the thief is chayev as if he did it himself - אין שליח לדבר עבירה. The gemara says that we compare tevicha to mechira, just as mechira requires the assistance of someone else, so too tevicha can be achieved through the assistance of someone else. The gemara seems to be saying that this is actually an exception to the rule, and we say that for tevicha - יש שליח לדבר עבירה, as if the thief himself did the tevicha.
There is a machlokes rashi and tosafos in kiddushin 42b ( i think that i blogged about it before), whether in a situation where the shli'ach is unaware that it is an aveira, whether we say יש שליח לדבר עבירה. Tosafos opinion is that there would be shlichus in that case to make the sender liable. Here too, Tosafos 79a (d.h. nasnu) points out that rather than saying tevicha is an exception to the rule of אין שליח לדבר עבירה, it could have said that the case is where the shli'ach is unaware that it is stolen, so that the sender (thief) would be liable to pay 4 or 5. According to Rashi, where the sender is never liable regardless of whether the shliach knew about it being stolen, it works out that we are forced to say that this case is an exception to the rule.
Why couldn't the gemara say that even though אין שליח לדבר עבירה (either because the shliach was aware that it was stolen, or like rashi that it doesn't matter whether he knew or not), the thief would still be chayev 4 or 5. The concept of אין שליח לדבר עבירה says that the aveira is violated by the shliach rather than by the sender, but nonetheless the shlichus is still in effect and it is as if the sender slaughtered the animal. From the fact that the gemara understands that this must be an exception to the rule of אין שליח לדבר עבירה, the gemara implies that when we say אין שליח לדבר עבירה the entire shlichus is void. Meaning, aside from not considering the averia to be violated by the sender, we break the shlichus entirely as if he were never sent by the sender. This issue is really dependent on 2 answers of Tosafos in Baba Metzia 10b, whether the shlichus is valid (implication of first answer) or void (second answer) in a case of an aveira. This gemara seems to imply that the shlichus is void which is a proof to Tosafos second answer.