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.