I make many folders with Mammoth Ivory and have to thin almost every piece. I usually take a small block of wood and attach some double sticky back tape to it. I then attach the mammoth piece with the bottom side out. This makes holding the piece a bit easier and keeps your hands away from the belts or disks. Very sharp belts will take of quite a bit of material real fast. If the piece starts to heat up, I use a small plate of aluminum as a quench plate. I just hold the piece down on the aluminum and it draws the heat out. I do this to keep the piece as cool as possible. As with other replies, you don't want the piece to get hot. You will not notice it right away but it will eventually start to stress and crack. Once I get the piece real close to it's final size, I soak it in Nelsonite for a day or two to seal it all up. They use Nelsonite to seal pool cues and Ive always had good luck with it. You can find smaller quantities of it at Ellis Knife Works.
http://refractory.elliscustomknifeworks.com/
Hope this helps
Bill