Yahbut, first you have to catch it.The most effective way to dispatch a possum is to use the broomstick method, same as if dispatching a chicken. Possum facing your feet, stout stick across the neck with your feet on either side. A quick, strong yank, jerking the tail upward and the neck pops. Death throes for a minute, then it's over.
Where (in the body) did you (OP) shoot the possum that didn't kill it? And did you only have two bullets? And why only "almost" cut off the head and not finish the job?
If you have a gun and need to kill an animal quickly, humanely and painlessly, aim for the center of the BRAIN. One shot is sufficient, if you do it right.