To use a saw to sever something (from something else). A noun or pronoun can be used between "saw" and "off." I had to saw off the lower limbs of the tree to keep my young kids from climbing it. The doctors had to saw the patient's gangrenous arm off.

slang Very disgruntled, angry, or outraged. Sometimes hyphenated. John was pretty sawed off when he found out that someone else had been given the promotion instead of him. There's no point in getting sawed-off over a bad grade on your exam. Just study harder next time!