From the wall, just break it enough so that you can get to the 'back' of the wall and make a large hole. Then start prying it off. Yes, you need to take out the wall down to the studs.
From the floor, I've used an ice chopper. You know, the one that you use outside in the Winter time to chop up the ice on you driveway and sidewalk? A flat-nosed shovel will work fine too. I'm assuming the floor tile is on, say, cement.