Relatively speaking - I did some sculpture in school and we played around with various stones - from Wiki
“Marble also has the advantage that, when first quarried, it is relatively soft and easy to work, refine, and polish.[1] As the finished marble ages, it becomes harder and more durable. Preference to the cheaper and less translucent limestone is based largely on the fineness of marble’s grain, which enables the sculptor to render minute detail in a manner not always possible with limestone; it is also more weather-resistant.”
- and its true, it is easier to carve than basalt for instance (which is a %*^%%), etc.
For rough shaping I assume they used hammers and chisels much like Michelangelo did.
They had saws likewise, I assume used with abrasives.
They had grindstones - i.e., they used stones to grind other stones using abrasives like volcanic sand, etc.
The pink marble facade comes from the same Tennessee quarries as used in the original neo-classic National Gallery.
The knife edge you see to the right of the photo has a 19 degree angle, the vertex of which has a slight chamfer. The overall finish of the stones is a light sand blast to mute the pink color.
That knife edge rising upwards is so startling that it draws people to touch it, rubbing their hands in wonder. Over the course of the first year or so human hands and skin oils polished a patch from eye level to about knee level to a smooth almost glossy sheen showing the natural deeper pink ofvthecstone. First reports from thw Museum staff believed them to be stains until more practiced eyes examined them.
So you see, working marble doesn't require special metal tools or grinding compounds.