rot off
1. To fall off of or away from something as a result of decomposition or decay. The disease causes patients' flesh to rot off in large patches. The door completely rotted off of the frame.
2. To cause something to fall off of or away from something as a result of decomposition or decay. In this usage, a noun or pronoun can be used between "rot" and "off." An infection in the tree is rotting its branches off. The moisture has been rotting off entire sections of the wall.
rot off
to decompose. If you don't clean and repaint that old windowsill, it will rot off. A few old branches finally rotted off, but the ancient tree looked as if it would survive the wet spell.