Trees regrow because they lay down dormant buds along the branches and trunks as they are growing, and some of those dormant buds then sprout after you cut them down. Doesn't matter when you cut down the tree as the buds will sprout if you are in the growing season. That being said, there are a fixed number of dormant buds and the closer to the ground you cut, the fewer buds available for regrowth. If you cut them down to the ground, some buds will sprout, others will not. Run over the new growth with a lawnmower a few times and the tree will use up all its dormant buds and die.