Islamic ruling on a few methods of slaughtering an animal:
(1) In Shariah-compliant slaughter (Zabh-e-Shar'i), it is necessary to cut at least three out of the four veins of the animal: Hulqum (the respiratory tract/windpipe, which is called the throat), Mari (the food and drink pipe from the throat to the stomach), and Wadajain (the two blood vessels that are on the right and left of the throat, called the jugular veins). In the case of cutting less than three veins, the slaughtered animal will not be Halal.
(2) After the soul has completely departed and when the animal becomes cold, its neck should be separated at that time. Separating the neck before it becomes cold, which causes pain to the animal, is Makruh (disliked).
(3) After slaughtering and before the animal becomes cold, cutting the vein of the neck bone with the tip of the knife, which causes pain to the animal, is Makruh (disliked).
(Book: Muntakhab Fatawa Darul Uloom Deoband / Pg: 452)