The particles in my diamond blade are bigger than dust. About the size of fine sand. It's a cheap blade though so there aren't too many, and it's imbedded in binder affixed to the surface of a steel disc instead of solid sintered. The particles only have to be in the outer layer, which would fit with seeder's hypothetical. Common sand is mostly quartz so it would abrade anything from quartz on down. That's what stocks used. It's been suggested they crushed flint is more efficient.
My idea would be to use an adhesive to bind a layer of abrasive to the outside of the saw the same way, so the bronze wouldn't even touch the stone.
The only drawback would be possible softening from friction.