"It finally quit movin' though, now that it bit itself," says our intrepid narrator.
And that, writes wildlife ecologist David Steen, could have something to do with the fact that a decapitated copperhead head can still inject venom. More importantly, if it did, the rest of the snake's body likely wouldn't have any special defense against that venom.
This isn't an area where there has been a lot of research and experimentation (just imagine the required permits!), but snakes do not have special immunity from their own venom. When venom is stored in a snake's body, it is located within specially-evolved glands that can safely contain it. This is the same basic idea that allows us to hold potentially harmful stuff in our appendix or gall bladder. If chemicals escaped from a snake's venom gland (or our appendix or gall bladder), it would be bad news.