Hey this is dangerous thread, I'm the second one to draw blood ! Hahaha
Seriously, I took my round dull pizza cutter over to my cheap electric can opener which has knife sharpener on the back side. I got the pizza cutter wheel spinning in that sharpener and ground both sides individually. Then I tested the blade by trying to slice a paper towel on my cutting board. It was not sharp enough to cut the paper towel..
Next I brought out my medium and fine knife sharpening stones and wet them down. I sharpened the pizza cutter by drawing it across the stone with one hand while applying downward pressure and spinning the wheel about 1/8th turn with the middle finger of my other hand. I repeated this motion maybe 20 times to ensure I got all the edges evenly. First the medium stone and then the fine stone. I did this on both sides of the blade. Now it will cut & cleanly slice the paper towel on the wooden cutting board, but I have to press very hard.
To me, it seemed sharper than before but not extremely sharp. This was my mistake. I was using this sharpened pizza cutter today and I accidentally pressed it into the keel if my hand and gave myself a nice cut. It cut the pizza better than ever, but I'm thinking it's not meant to be so sharp due to the danger of the open round blade and it probably does not really need to be all that sharp to cut pizza.
Bottom line. if you sharpen your pizza cutter be extra careful not to cut yourself!