No.

Final Fantasy has always been about groups of people teaming up to save the world from an evil force - it has never been about players killing each other in them. This is why PvP in this game is basic and separate from the main game, as it is not the game's focus. If you are wanting to fight other players and kill them in the game, then you are playing the wrong game I'm afraid, as FFXIV will never allow that.