Daf Yomi - Yoma 64 - Is Stoning a Shechita too?

Our Gemora states that the 'pushing off the cliff' by the שעיר המשתלח is considered like a שחיטה. The רשש in Pesachim and the Minchas Chinuch ask why do we not say this concept by שור הנסקל as well. Let us say that the stoning of the ox constitutes a שחיטה and one should be prohibited from shechting the son on that day? Reb Chaim Ozer answers that this rule only applies by a mitzva, however by a punishment it does not.