Is it possible to cut yourself on pyrite?
The Wikipedia page for Mohs scale shows that pyrite has a hardness of 6-7 (according to the page on pyrite, it's 6-6.5) while plate glass has a hardness of 5.5 and a pocketknife has 5.1. I've cut myself on both knives and glass before, so I'd wager that pyrite should be able to slice.

The catch is that I've never cut myself on a cube of glass or a cube of steel before--a 90 degree edge just doesn't generate enough pressure for that. So either your pyrite must have very nice serrations on the edge or it must have an edge sharper than 90 degrees.

Is that possible? I don't know. I suppose at this point you could invoke the leeway granted to you by fiction.