splinter off (of) (something)
To tear, chip, or break off of a larger piece or thing. Wood began splintering off around the bullet holes. The impact has caused a piece of bone to splinter off of your femur, and it will unfortunately require surgery to repair.
splinter off (of) (something)
and splinter off (from something)[for a bit of something] to tear off or separate from something. (Of is usually retained before pronouns.) A piece of wood splintered off of the oar and dropped into the water. A tiny bit splintered off and stuck in my hand.