Granite dust is dropped by the Grotesque Guardians that can be found on the Slayer Tower's rooftop.
With 50 Smithing, the dust can be used on cannonballs to create granite cannonballs. When creating them, a message asks how many the player would like to make. The stack of granite cannonballs is made instantly regardless of quantity, and a message in the chatbox will state You apply a thick coating of granite dust to your cannonballs. No Smithing experience is granted for doing so.
Granite cannonballs are the superior ammunition for the dwarf multicannon, which increases their max hit from 30 to 35.
For an exhaustive list of all known sources for this item, see here