I am not a complete idiot, and some parts are missing!

This sentence should be an American joke, literally meaning "I'm not a complete idiot, I lost something."

It can be understood as saying "I am not a complete (complete) idiot" first, as if to show that I am not an idiot, but have a brain; But with this sentence, "(that's because) some parts (parts) are missing." It shows that he is not a complete idiot, not because he is not an idiot, but because he is not complete enough. This is a kind of humor.