Try cleaning with a 10:1 water:chlorine mixture. If the stains have set in over time you may need to have a professional with acid clean and seal the stone.
Using backing soda and water to make a paste is always a good cleaning solution for natural surfaces. Make a paste and allow it to sit on the surface for several hours at the most. You can even cover it in plastic wrap to keep it damp. Wipe it down with water and soft cloth.
The best way to get that answer would be to find a professional to ask they deal with it so they would know how to remove stains or if it is even possible to do it.
There is a special soap designed for specially for cleaning stone. This will work if the stain is light and not very deep but commercial stain remover are available if the stain will not come out with the soap.