Acturally, the idiom should be "Don't let the door hit you on your way out."
Meaning:
1. Get out, you are not welcomed here anymore.
2. Conversation over, get out!
The intention is not to let the door hit someone on his/her way out. Rather, the speakers's intention is to tell the other party to get out in a sarcastic way.
為甚麼是Don't let the door hit you on your way out,是因為若門打開後,你稍有停留,門就會碰到你,若俗一點的說法是"Don't let the door hit you on your ass"
2013-06-14 18:29:04 補充:
如:
When Peter had a fight with the teacher, the teacher kindly asked him to leave by saying, "Yeah, Don't let the door hit you on the ass, buddy."
但你的句子是let the door hit you on your way out, 其意則與don't let the door hit you on your way out.相反