Hi and welcome to the Nut house.!! . . . . No one around here will bat an eyelid at your suggestion of cutting slate has it's been done many times.
Personaly I've never cut slate but I have cut Granite and Marble which are along the same lines regards cutting.! . . . Nothing difficult just Loads of water and Diamond coated cutters or burrs. Thou I think for engraving slate you'll get away with Carbide cutters.?
Speeds and feeds took me a good while to get right because of the relatively high spindle speeds and is machine/material dependant.

I found the Secret to success and tool life was loads and loads of water to cool and flush away the slurry.!! . . . Be warned thou it's a messy job and slurry can be quite destructive to machine so prepare well.!!