Parashas Vayikra · Aliyah 1 · Passuk 5
Chabad.org — English translation + Rashi
Torah Temima points to Chullin 27a and Chullin 30b (verified; slaughter at the neck; drawing motion of the knife).
E-Daf — Chullin 27a · E-Daf — Chullin 30b
English: Rav Kahana said: From where do we know that slaughter is at the neck? As it is stated “and he shall slaughter” — from the place where one “cleanses / draws.” The school of Rabbi Yishmael taught: “And he shall slaughter” means only “and he shall draw [the knife]”… From here: if one severed the head in a single stroke, it is invalid.
Custom (etymology / word-play on shachat) — the verb teaches both the place (neck) and the required back-and-forth drawing motion of the knife.
Kosher slaughter is performed at the neck with a drawing motion of the knife. Chopping the head off in one blow is invalid.