Razor

Razor was a henchman of the Joker who was present during the events of Batman: Arkham Asylum. He was an inmate of Blackgate Prison and was shipped to Arkham Asylum after a 'mysterious' fire at Blackgate.

Arkham Asylum Incident
After he was shipped to Arkham Asylum, Razor was first seen when the prisoners locked Aaron Cash and Dr. Stephen Kellerman in a Joker-gas infected room. One of the thugs talking to the Joker via a walkie-talkie mentioned that Razor was still in the room. The Joker then remarked that he was too slow. When Batman went up through the ventilation system and entered the room flooded with Joker Gas, he saw an inmate struggling on a line above a weak roof to a cubicle. Batman was forced to cut Razor down with a Batarang to get to the control panel to get rid of the gas.

Razor somehow survived. When Batman re-entered the Intensive Treatment Center, Razor and a group of other henchmen were finishing up wiring the gargoyles with bombs. As Razor was finishing up with his assigned gargoyle, Joker "tested" the bombs, and killed Razor.

Arkham City Incident
In Arkham City, another thug named Razor left Joker for the Penguin, but was ultimately killed by being dropped into a pool of razor blades (Possibly a pun because of his name). A team of Penguin's Henchmen remarked on that and said that Razor should never have left Joker, because the Penguin was always going to weed information out of him.