You kinda fumbled this. The dig was sufficiently obvious after the second sentence. Third one killed it. You may as well have added a fourth sentence, "And by that I mean, your mouth is an asshole because everything that you say is shit, figuratively speaking."
Don't get me wrong, it certainly wouldn't have won points for originality in any case. However, no matter how pedestrian or clichéd the insult, it's still painful to see it executed so artlessly.