Killing off a player's character is an easy way to kill off an RP itself due to people thinking that they're being targeted. People will take time and effort to create their characters and naturally they want them to survive as much as possible to hopefully be the hero in the end. It's a neat idea by all means and would be great in a Hunger Games like Roleplay, but that what you as the GM would have to do is sever that connection between the Player and Character from the get go.

Thinking about it and like what was touched on above, you will probably find that a small, or very small group would work well, and maybe they have to create multiple characters. Let's say you have 5 players with 3 characters each. That's 15 possible characters to kill off. Not all have to die in the end, but the magnitude of knowing that your character may "die" is a fear that could keep the RP going for a long time.

I would also suggest playing, or watching Danganronpa (Game and Anime). It's a school where the students have to kill each other and starts off with 16 but ends with about 5 who survive. Even though 5 people survive, it has you hooked from the get go because that character you may like just may die in the next scenario.