Sorry to be so ignorant about this, but if the diamond is the hardest known stone, what stone is/was used to cut diamonds?
Other diamonds. Any material of the same hardness will -- eventually -- abrade a stone. But some diamonds are harder than others for reasons too complex to go into here. Early cutters quickly learned and benefited from that fact. Still, diamond-cutting is a very slow proposition. It's a highly specialized craft and is quite different from the techniques used to cut other gems.