Unless you’re working on a very hard stone I suggest you wrap your seal stone in a bit of cloth, tissue, or soft leather before you clamp it into your seal vise.
Most seal vise are made of wood, which should be softer than your stone, but you don’t want to take a chance on scratching or bruising your stone. On the other hand, if you’re holding the stone in your hand while carving you should remove any rings or jewelry and be sure to keep your fingernails trimmed short and neat. A soft stone can be easily and inadvertently scratched even by a fingernail.