Oh, nice - thanks for this. Kinda torn on the story-
On one hand I don't see why the Joker wouldn't cut the Fam's faces off. He's insane and has no inhibitions whatsoever. It was hinted at by Harley, and in the story that this Joker was more violent, sadistic (?), and dangerous. At the very least, didn't he mention he was pouring Ammonia in Alfred's eyes at some point to Batman? But Alfred looked fine. But on the other hand I'm glad no one in the Family was taken out.
And I take it we are supposed to assume that his memory was extremely selective while he was stalking/harassing Nightwing and Batgirl in the same way he was when he took Alfred from Bruce?
Well it's confirmed by Bruce that he all but told Joker that he was Batman, but that Joker didn't care. Even though he ignored Bruce at the time, he still knew so it makes a bit of sense that he would use Bruce's family to go after Batman. Joker would never go after Bruce, he couldn't give two shits about him. But he sure as hell would do whatever it took to hit Batman.
I think Joker didn't mutilate the family because frankly unless he could make it a joke it doesn't really fit his MO. Even early on in the arc you can find the joke in all of his attacks so long as you look for it. Mutilating them himself wouldn't be as bad as them killing each other, nowhere near as funny either.