I am having trouble grinding a marble tile floor flat. It seems that the tiles are cracking at the corners, why is this happening?

Sounds like you are dealing with a tile floor that has not been installed properly. A poorly installed tile will sound hollow when you tap it with a broom handle . The hollow sound is an air pocket under the tile. The material that the tile is set in is not completely covering the tile in these pockets. This is a weak area and will crack when enough force is placed on the tile. Before you begin any grinding job it is a good idea to sound the floor to determine how much of the floor is hollow. If there are many hollow tiles, you can assume that you will break some of them. If this is the case you will have to plan on replacing those tiles or do not grind the floor. Try a light honing instead.