Thanks for your reply, Dave. I have an Old Stone OvenŽ from Kitchen Supply Company.
I've just received a response from the retailer which said "It is normal for the stone to accumulate stains from drippings. This will not alter the taste of your pizza or bread. However, cooking residue may smoke and create odors. A scouring pad will remove most
burned on bits. If the accumulation is heavy, then a thorough sanding with a hard abrasive, like emery paper, may be necessary. Small stains can be removed by scrubbing with a toothbrush and a paste made of baking soda and water."
They also said "No, you may not leave it in the oven while in the self-clean cycle."