You can use organic solvents or for a more vigorous cleaning acids. You might want to use a covered container,as these preperations can evaporate in air,and leave a residue worse then the original problems. If you find the solvents do not remove the contaminants you can use acids. Caution when using and disposing of these acids. After the acid treatment,a washing with soap and water,and in some cases a bath in a neutralizing solution.
Some acids can have a delayed discoloring chemical reaction.
So must be neutralized in solutions of say,vinegar and water or baking soda. Consult a mineral cleaning expert. Or more effective is to place the stone in a vacuum,and insert the treatment medium while still under the vacuum and with pressure. Again,all of this is done under mild heating,to both open the pores of the stone,drive off any remaining water,and in some cases the medium material must be heated to remain liquid. A simple chamber can be constucted inexpensively using a plastic or glass bell jar type cover,a hot plate,and hydrolic piston assembly.