How do I cut Natural Stone Tile?

Use a wet saw with a diamond blade and go slow pushing too quickly will cause cracks. You shouldn't really have to push at all just let the blade eat through the stone at its own pace. When making rounded cuts you have to make several small straight cuts with a wet saw also you can use a diamond drill /hole saw for holes just remember to use plenty of water to avoid heat fractures of the stone.

A good tile water saw with a good seraded stone blade. Unfortunately the blades are about $125 bucks but last a long time and do a great job. Dont use the little portable tile saw they tend to slow down under pressure and vibrate too much causing tiles to break easier.

Try a diamond disc cutter

A wet saw. You can rent them too!

High speed water grinder.