Cleaning stone tile & grout- Any ideas of what I can safely clean it??

Can't ever go wrong with baking soda, vinegar and good old fashioned elbow grease. After that they do make natural stone sealers that might help keep the mold from coming back.

I agree with sealing it after getting it clean. Baking soda, peroxide and dish soap also works well. Try it out on a test spot that is not very visible to make sure it doesn't mar the surface.

the stone should have been sealed after installation. Do you have a exhaust fan ? Make a mixture of baking soda and water into a paste and apply to the mold first,because it is stone I would not use anything acidic.

Baking soda/vinegar combo is my go to cleaner. So easy and effective!