What I have done is to disassemble the pizza cutter and chuck it up on a shouldered bolt in my drill press. I can then bring in a stone to dress the edge, then flip it over and repeat.
Alternatively, there was an Amish gentleman that always did an amazing sharpening job on my saws, but I'm not sure if he would sharpen pizza cutters. <grin> I found him while riding my motorcycle around northeast of town by their farms and asking around for someone who could sharpen a saw for me. Unfortunately, I couldn't possibly give you directions; first, I don't remember, but more importantly, the street signs out that way always seem to disappear.
ps-I cut in an aluminum pizza pan also.