Granite and other igneous stones are generally not good sharpening stones, and sedimentary is preferred. Granite itself, especially the stuff we have here in Maine, is far too coarse in its "natural grain" to cut well when used in its native texture, but becomes too glassy when ground/polished, and you'd end up producing such an effect if grinding two granite stones against one another. The only way I can think of making a usable sharpening stone from granite would be by lapping it with loose SiC or diamond grit to create a "blasted" texture that would work somewhat like sandpaper or a file, but once the surface blunted you'd need to recondition it again. And it's very irregular in its mineral distribution and size. Altogether not a strong contender. Works great as a lapping plate if you get a tile of the stuff, though!
Granite may not work well, but we do have lots of siltstone and schists, and the siltstones have a lot of quartz while the schists have garnet in them. Both will more readily break down to expose fresh grit in use and tend to be more uniform in their grain size/distribution.
