Can someone explain why they cut off Herschel's leg if everyone is already infected? Does getting bit speed up the transition to zombie by combining whatever is in the air and possible zombie fluids to the blood stream? Right now my understanding is they only become a zombie once they are dead.

Can someone explain why they cut off Herschel's leg if everyone is already infected? Does getting bit speed up the transition to zombie by combining whatever is in the air and possible zombie fluids to the blood stream? Right now my understanding is they only become a zombie once they are dead.