I think, You will facing a lot of troubles of the Dust/sand from the marble machining. In my experience, its deadly for all precision equipment, if you put sand in it, therefore take a lot of care for protecting the sliders, ball bearing etc. from dust and marble slurry.
I guess, fore stone machining, diamond tools are the right try, like for engraving glass etc. You even can try different tools with a Dremel by hand to see, if it will work. Normally, the hard particles in stone will grind all tools away in short time.