Razor

Razor was one of the Joker's

Batman: Arkham Asylum
He was an inmate of Blackgate Prison, and was shipped to Arkham after a mysterious fire at Blackgate. Razor is first seen when the prisoners lock Aaron Cash and a doctor in a Joker-gas infected room. One of them mentions that Razor is still in there. Joker remarks, "He was too slow." When Batman goes up through the ventilation system and enters the room flooded with gas, he sees an inmate, presumably Razor, struggling on a line. Batman is forced to cut Razor down to get to the control panel. Razor somehow survives, as when Batman re-enters Intensive Treatment, Razor and a group of other henchmen are finishing up wiring the gargoyles with bombs. As Razor is finishing up his assigned gargoyle, Joker "tests" the bombs, knocking Razor off of the gargoyle.

Batman: Arkham City
Razor is mentioned when Batman is resucing Captain Miller from the Penguin's goons. When entering the room that Mr. Freeze's suit is kept in, two of Penguin's men talk about Razor being killed by Two-Face for not giving information about the Joker.

Trivia

 * It is arguable that the "Razor" that Two-Face killed is different than the one in the asylum, due to the fact that when you use Detective Mode on Razor when he is knocked off the gargoyle, it says he is deceased.