The ones in the ground are generally easier to get rid of. The fact that they're connected underground means I can tear up a whole string of them. I've actually cleaned that tree of them before and they still come back. The roots are so tough to pull out - they're much stronger than you would think. But you have a point, if I kept cutting the foliage they wouldn't have a way to photosynthesize any food and would die off, right? I also have some growing over in the side yard where it's pretty shady and they're away from nearly all of my butterfly plants. Maybe I can do a test over there and see if a weed killer would kill them without say, killing the grass or other weeds around them. I hate to resort to chemicals, but even I admit you sometimes have to use them sparingly. Although, it's usually wasp spray and fire ants I'm trying to kill, not plants.