For that money and probably a bit more you could build one for engraving, but definitely not for cutting. Say 120x120cm. , bed must be low, gantry sides raised. Overbuild gantry and Z. 3kw spindle will do the engraving, no problem. Wet of course, or sth like a mist system. Stone could be machined dry, but lower tool life and you have to have a good vacuum system and shoe.
Again, only engraving. shallow pocketing and probably shallow 3d jobs.

Now the challenge is - how big a slab you would deal with. With anything over 50kg i would say you are looking at 10k at least spent.


Damn that X Carve stupid videos, these people should be blocked from youtube.


Now there are impact engraving machines and laser engraving machines, that are light cheap and not so cheap/ the laser ones/ that may suit you better as they are focused on producing exactly that niche products.