Can I grind down natural slate tiles using diamond floor grinder?
A floor grinder will grind slate. Slate is comparatively soft and, though you wouldn’t expect it, soft materials cause faster wear than hard materials on diamond faced tools – well, they do on angle grinder discs anyway. Expect a dull surface afterwards rather than polished, though it might be possible to polish it to some extent. I’m not sure who you could get to do this. DIY is possible but you risk spoiling the floor. I would have thought a stone flooring specialist or one of those company’s that sell stone slices for interior decorative use would be able to help you.
