I have two plum trees that produce suckers like crazy. I know these are supposed to be removed promptly, but my life has been pretty hectic for the past several years, and I just let them grow. One tree has filled an area about 4x6 feet with suckers so dense and thick that I can't step through them.

So I've got two questions. One: should I cut the suckers off all at once, or gradually? If gradually, how gradually? I keep reading that "suckers only divert nutrients that your tree needs for healthy growth," but nutrients come from photosynthesis, and if I remove all of the suckers at once, the tree is suddenly going to have a lot fewer leaves to photosynthesize with. I wonder whether that's healthy.

The second question is, what can I do to prevent the trees from producing a whole new crop of suckers? Or if I can't stop them, at least slow them down?