Answers:
Don't use detergent .Set the oven to it's highest heat for about an hour after use a scraper or a grill brick on it.A little water is ok but simply pour it on if you submerge it or hose it while it's hot it will crack.Oh yeah,clean it while it's hot,and to be honest a pizza stone doesn't hold to be spotless.
Other Answers:
I worked at a place that cleared everything out of their oven on a Monday morning about once a year and brought contained by a power washer. Spray it down with oven cleaner, agree to that sit a while, then stir to it. Wear goggles and ear plugs and try to not get splashed next to the oven cleaner.
Just use a commercial oven cleaner (they deal in them near the adjectives purpose cleaners) and leave it within on the oven's self-cleaning cycle. The chemical compounds that are holding the grime to the stone will burn up and all you'll enjoy to do is wipe away the charchol.