This can be done a couple of ways. One is to purchase a "grout removal tool." This is a small hand tool with a rough carbide edge and is very inexpensive from one of the home improvement stores. Tool is found in the tile dept. The problem with this tool is it is somewhat labor intensive since it is simply gouged up and down and around the grout lines of the tile you want to remove. The other method is to use a hand grinder or a hand drill. With this method you would attach a masonry cutting disc and run the disc (carefully to stay in the grout lines) around the damaged tile. Safety glasses should be worn using this cutting approach.
For both approaches the grout is only removed to about 3/4 ths of the depth. At this point a firm hammer blow is directed to the center of the damaged tile. The tile will break up into pieces and these will sometimes just lift off or some may need to be pried up with a stiff putty knife or even tapped gently with a chisel. Once the tile is all removed you may need a propane torch to heat the left over adhesive so most of it can be scraped off. A hair dryer might work but is a much slower process. The heating wires under the tile are not right on the surface so by being careful there should be no damage to them.
Dennis (cut2it)
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C&onstructi&on C&onsultant
Over 40 yrs. as General Contractor for new const. & remodel - retired with time for you.