Put on safety glasses and a dust mask. Install a grinding wheel into a hand-held rotary tool. Use a wheel that is appropriate for grinding stone or masonry.
Place the grinder onto the grout line directly beside the damaged tile and hold it in place until it grinds it down. Move the tool upward to continue removing the grout until the entire side of the tile is free.
Repeat the process on each of the other three sides of the tile so that no grout remains along the sides.
Place a small chisel in the center of the damaged tile and tap the head of the chisel firmly but gently with a hammer. Continue tapping it until the tile starts to break and part of it falls free from the wall.
Reposition the chisel so that the blade is under the tile in the area that broke off. Lean the handle of the chisel toward the wall at an angle and tap it with the hammer to drive the blade under the tile.
Continue chipping away at the tile until all of the pieces are off.
Place the grinding wheel of the rotary tool back onto the wall and use it to grind off any of the thinset that was behind the tile.