I have large granite tiles on my counter that don't go all the way to the edge. Ceramic ones complete the lip. Unfortunately, to get my old dishwasher out from under the counter I had to break some. How do I remove what's left of them without damaging the really nice granite ones? Is there anything else I need to be careful about?
Visit your local flooring company for visual help in understanding how to remove the tiles. There are several tools available that have been developed for just this type of work. Be prepared however to loose a fair amount of the currently undamaged tiles, how many depends upon how careful you are combined with how well they were installed in the beginning. At this point you are hoping for a poor job. Remember however that you can cut down any tiles that you have the pieces of and make a new mosaic out of them. Broken tiles are never a complete loss.
The force from removing the broken tile can be transferred through the grout onto the granite tile. So first try to clear out the grout between the 2 rows of tile. Use a hammer and chisel (and safety glasses) and swing away from the tile you want to keep. If there is a mud job with thinset between the mud and the tile, try to chisel the thinset off, leaving the bottom mud-job in tact. If you're lucky, you won't have to repair it and can start laying the new tile right away.