When you make a really stupid mistake, or when you fall flat on your face.
Billy was derping out when he thought his lunchbox was his textbook.
John derped out after getting dizzy.
Matt's derping out!
Bob derped out!
When you're about to say "Son of a bitch" but stop yourself halfway through to say something else, usually another instance of swearing, or get interrupted.
Person one: Son of a-
Person two: What? Gone mute?
Person one: Ya know what? Fuck off richard!
Son of a- Im gonna destroy you!