What does "Because shut up, that's why" mean?
It's a really rude way for someone to try to block the other person from continueing to talk or to stop the whole conversation.The person isn't giving a single reason why they want the other one to shut up, because they're probably annoyed or offended.
I don't think I've ever heard anyone say exactly that, though I can certainly imagine it being said.
If one were told to do anything, and one asked why before complying, the impatient, authoritarian response could be: Because _______, that's why.
The responder is saying that he doesn't have to give any explanation or reason for giving the order.
Because "sit down", that's why.
In the English of SE Pennsylvania where I live, I think I would more likely hear:
"Because I said so", but the "Do it, and don't question why" meaning is the same.