It is easier to have success with smaller holes. This question is usually asked about 4 inches or larger.
When you drill larger holes, the remaining tile becomes weaker due to the material removed.
There are two main remedies for this issue:
1- You need to be more patient and apply less (far less pressure). The diamond hole saw would lightly grind away the material with minimum pressure on the tile.
2- The tile has to be laid on a flat surface, possibly with a towel underneath, so that when you apply light pressure with the diamond hole saw, it will be supported at the bottom.
You can see one of our professional clients drilling a 7-inch hole with our diamond hole saw in this video.