When you have a teammate that is annoying you during a Hardcore match, first make sure you do not have Stopping Power. Next, take your pistol and fire a shot into their legs. In most cases, if you make it look like you did it on purpose, they will kill you. This is what you want as it will show up on people's screen that that player just killed a teammate. Find the player and repeat this. If they kill you again, repeat this a third time and the game will auto-kill them while the rest of your team will assume the player is a Team Killer and may help you kill him. This should frustrate the player enough to make them leave the game, all without you being penalize.
As host of a game, press PlayStation Logo to bring up the Cross Media Bar menu. Go to "Friends List", find the "Players Met" menu, and look for the player that is annoying you. Press Triangle on their name and add them to your "Block List" to kick them from the game. If you are a host, players on your Block List are unable to play a game with you and are thus automatically booted from the game.