Stone is a Composition Type that's extremely resistant to most physical and magical damage (+12 per level for armor at base) but extremely vulnerable to explosives and the spells Shatter and Exploding Brain. It also has a 9 in 10 chance of being successfully transmogged into Flesh.
Transmogging your dwarf into stone will kill him instantly, which is one reason why a transmog cast directly on your dwarf will only turn him to flesh-- otherwise, it could make for some cheap deaths, even by Dwarf Hammer standards. (Bouncing a transmog off a glass creature, on the other hand...)
The gorgon's stare will turn the player into stone, though this is not the same as a transmog.