splinter off (from something)

1. To tear, chip, or break off from a larger piece or thing. Wood began splintering off around the bullet holes. The impact has caused a piece of bone to splinter off from your femur, and it will unfortunately require surgery to repair.

2. To separate or depart from a larger group with divergent ideas, ideology, goals, plans, etc. The group of radicals splintered off from the orthodox church and formed a new ministry based on religious extremism. We decided to splinter off from the main group so that we could focus our attention onto the matters we thought most important.

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.