By the way, as others have said, that stone does indeed look like a La Grise. Your description of how it behaves would confirm that.
La Grise's are slow cutters: with a fast cutter the slurry would turn black soon, with the La Grise I used, the slurry never turned black but remained grey. By the way, when finishing on my La Grise (it auto-slurries as well), I rinse the stone a lot so there's no slurry at all on the stone