Are you thinking somethng like this with a flat full disc contact?
https://www.youtube.com/watch?v=aB8601i0hJ8
I'd be careful about a regular stone grinding disc. I've done it on hard concrete and it's okay-ish, but i think slate is softer and more fractious and the stone grinding discs are quite aggressive.
You could also try a hand held belt sander probably more for rough flattening than finishing.
you might get better speed control with that.
Or go to the tool hire place and see about hiring a proper concrete grinder/polisher.
I hope you can move the work outside because it will create a lot of dust.
the guy in the video uses water which is probably a good idea.