the dollmaker removed joker's face, in detective comics #1. the reasoning or logic hasn't really been detailed yet. but the skinned-face-attached-to-real-face artwork capullo put out during the death in the family run was friggin awesome. joker looked a whole new level of awesome.
They ever bother to explain how someone can live with his face removed and why the skin hasn't rotted while it's hanging there?
And don't say "it's comics." They ought to have at least some explanation, even if it were that it was a side effect of the chemicals he fell into as the Red Hood/Jack Napier. Of course, either way they've now basically given Mr. J a superpower.