Assuming you're asking about killing Serana, you can do it, but you need to use the console a bit first.
The first thing you'll want to do is find your load order of Dawnguard.
Since Serana is essential you'll want to remove that by bringing up the console through the '~' button. Then enter: 'setessential xx002B6C 0'
The 'xx' is the location of your Dawnguard in the load order. If you need more help on that see 'base ID's' on the elder scrolls wiki.
After that she's just a normal npc, capable of dying, and you can have your go at it however you want. Although, all of this said, I'm not sure why you'd want to axe off this particular character, she is, in my own opinion, one of the best characters in Skyrim, next to Miraak, of course!
