I don't remove the paper, it's thin and the stone is hot, so the bottom is crispy. To retrieve the pizza, I pull it out with the paper onto the chopping board, ably held by my trusty assistant.
I learned the hard way that merely trying to carry the pizza to the counter by holding the paper is successful till it isn't, and the paper tears. While my ninja reflexes meant I caught the pizza, the downside was that I was then holding a very hot thing.