The meaning of: "Why don't you just beat it?"
It means "why don't you leave?", and comes from "beat a retreat", which itself comes from the use of drums to signal soldiers to leave the battle field.
Find it all here: http://www.phrases.org.uk/meanings/58800.html
"Beat it" has various other mainly sexual meanings, so it depends on the context. See here: http://www.urbandictionary.com/define.php?term=beat+it