It looks like it could be a weedy fruit tree, like a pear, crabapple, or cherry. When I moved here almost 15 years ago there was crabapple sprouts like that all over my front yard. Somebody had covered the stump area with plastic and mulch but it hadn't done much good. I just snipped the sprouts every time I saw them, as soon as I saw them and they stopped coming up after a couple of years. I'll be interested to see if anybody else has a better (or faster) way of getting rid of it.

Jeanne

I second Jeanne's post. It could very well be sprouts from the root system of a tree that was cut down, and cutting the sprouts down just under the ground level should, eventually, exhaust the rootstock. Cut them off as soon as you see them, as Jeanne said, and you'll win.