I have the same problem and need to remove the tile, durock / cement board as well as the subfloor due to water leaks and mold. Nothing is easy about this job, but scoring the floor with a skill saw cement blade has certainly helped by making the job a little more manageable. Open windows, block all vents and mask required! Back to work. . .
Bounce a golf ball all across your floor. You will hear the hollow spots. If your bad tile was not an exception, give the contractor a chance to fix it. He may have been screwed by a bad subcontractor. If he doesn't, get ready to go to the state license board, and maybe small claims court.
I've never seen tile installed this way. I've seen installers glob it down, but then trowel it out. Tile needs to be installed on a flat, sound surface or it will "bend" and will break or loosen over time. what type of guarantees did you get from them? I'd put them on notice and get them out there when the next tile pops off.