You can cut down apple trees with an axe. You will get one log and two or three apples from each apple tree that is cut down.
You could cut down the apple trees to get the apples, but hitting the trees with the mallets will give you apples without losing the trees. If you cut down the apple trees you would have to dig holes and plant apples in the holes and wait for the apple trees to grow again. It's faster to just use the mallets.