Daf Yomi - Yoma 64 - Chopping its Head as a Shechita

Tosfos discusses if we can equate the concept we have by the שעיר המשתלח to an עגלה ערופה.There is a din if we find a corpse of a man that has been murdered between two cities and we can not verify the killer, we must bring a calf and cut off its head and that serves as an atonement. Do we say there that the cutting of its head constitutes a shechita and therefore it will not be considered a neveila and there would be the איסור of אותו ואת בנו and we would not be allowed to shecht its mother.

The Minchas Chinuch asks on a ruling of the Rambam. The Rambam states that if one is shochet the calf, there would be an issur to shecht the mother. Why doesn't the Rambam teach us a bigger chidush, that if he chops off its head it is deemed to be a shechita and there would be that prohibition?

Rav Rudderman in his Sefer Avodas Levi answers that this concept that something can be considered a shechita (even though it isn't) can only be by something that is in the regular category of kodoshim where we find the concept of shechita. This would be applicable to the שעיר המשתלח. However, the עגלה ערופה is in a category of kodoshim all by itself and there we do not find shechita, so the chopping off of its head cannot be considered a shechita. He adds that this is true by the melikah of a kodoshim bird as well.