Charles Ellicott Commentary Leviticus 5:8

"And he shall bring them unto the priest, who shall offer that which is for the sin-offering first, and wring off its head from its neck, but shall not divide it asunder:" — Leviticus 5:8 (ASV)

And wring off his head. —For the manner in which this was performed, see Leviticus 1:15. It should be noted that it is distinctly ordered here that in this operation, the head of the bird is not to be severed from its body. In this respect, it differed from the burnt offering described in Leviticus 1:15.

At the time of the Second Temple, the priest went to the southwest horn of the altar. He held the two feet of the bird between two fingers and the two wings between two fingers. He then stretched out the victim's neck to the breadth of his two fingers and cut it with his thumbnail, breaking open the great blood vessel at the neck.