I had a similar problem with a tiled fireplace. I wanted to replace the ugly patterned tiles on the hearth with plain ones from the surround that I was getting rid of.
It was a hit-and-miss affair. Some broke and some didn't, but I got enough off whole to replace the patterned ones. I just put a wallpaper scraper between the tile and the wall, held it as flat to the wall as it would go, and tapped the handle very gently with a hammer until the tile came away. I'd imagine hardware stores probably sell something more robust that's made for the job, but the wallpaper scraper did an adequate job for my purposes.