Well.. you can't really kill Claire. I mean, you could put her into a semi-permanent coma. But if anyone was to ever remove the bullet from her brain or whatever else may have been jammed back there she'd just come back to life.
It kind of bothered me that on the last season in Peter's Mother's dream that it showed that Clair was dead because her head got ripped off. While I'm sure she might have been initially dead due to that, we all know how her powers work. I'm pretty sure that after some time she would "wake up" and start regenerating the rest of her body. The only way that wouldn't work would be to damage her brain in the right spot, somehow.
And besides, you'll never be rid of Hayden :3 she's too smexy.