Cut, do not pull
Pulling a support tears it away along whatever path is weakest, which is frequently through the part surface rather than the interface layer. Flush cutters let you sever the support where it meets the part and then lift it away with no tension on the surface.
Work from the outermost supports inward. Removing the outside first gives the remaining structure somewhere to flex, which lowers the chance of levering against a thin wall.
Elephant foot and the first-layer edge
The bottom edge of a print is usually slightly wider than the rest, because the first layer is squashed into the plate. That lip stops flat parts sitting flush and stops parts mating properly.
A rotating deburring tool takes it off in one pass and follows the edge without digging in, which is exactly what a knife does not do. It is also the right tool for the inside of printed holes, where a chamfer helps a bolt start straight.
When to fix it in the slicer instead
If supports fuse to the part, raise the support Z distance so the interface is not welded on. If they snap off leaving stubs, they were too sparse. If they mark the surface badly on a part that matters, print it in a different orientation so the surface faces up.
A part that needs twenty minutes of cleanup every time is a slicing problem wearing a post-processing costume.
