Ugh, brings me back to my first experience with a blending stump & pencil sharpener

For minor sharpening or to remove excess graphite/charcoal, hone the blending stump against a sanding block. You can pick one of these up at an art supply store for about a dollar. It's a small hand held paddle with a few sheets of sandpaper stapled to the end. Great for touching up the shape of a pencil tip or blending stump.

For a major re-sharpening on a blending stump, you either need to use a craft knife to whittle it to a point, or just buy a new one if you're inclined. (The sanding block really works great if you use it regularly.)

Hope that helps!