I think the accuracy is funnier than the structure of the joke itself. I can't tell you how many times I've had to clarify things that I've said right after I've said them because the stutter changes the whole meaning. The worst is I have a habit of saying "uhh" before a word I know I will stutter on. Which is fine in most cases, except when people ask what I think of something. "You look uhh.. nice today".