How to keep my pizza stone from smoking?
(1) Wikihow suggests "As a last resort, soak your stone in water," and also "Baking soda is a sodium bicarbonate and is great for cleaning off dirt and grease," and lastly, an a one-shot hail mary, "Using The Self-Cleaning Function."

http://www.wikihow.com/Clean-a-Pizza-Stone

(2) Caveat: I've not tried any of these methods myself.  I bake pizza on a flat cast iron pan, which I use for everything else.  It works fine, you can put a bit of oil on the bottom of the pan.