Does shearing a sheep’s wool hurt the sheep in any way? If it did hurt the sheep, could you just “trim” the wool instead of taking it all off?

No. It’s like you getting a haircut.

Trimming is the same as cutting, in hair terms – except less hair is removed. Trimming wool does not help the sheep; it leaves most of the wool in place which is uncomfortable and unhealthy. In addition, the trimmed wool ends would be too short to have any commercial value and would end up in landfill. As wool flocks would no longer have any commercial value, thousands of sheep farmers would go out of business and their flocks would be slaughtered. Those industries dependent on sheep wool would have to turn instead to synthetic alternatives which are very damaging to the environment.

Quora linky.