If they're in the lawn, continued mowing will eventually kill them.  You can also use  an herbicide and paint it on the sprout with a brush.  See the statement below from Washington State University about how to do this:

Suckers that keep coming up from the root system of a cut-down tree can also be treated with a brush killer. If the suckers come up in a lawn area, you’ll have to spray them with an herbicide that will be absorbed by them but will not harm the grass. Sprouts coming up in an area where you don’t need to be concerned with good plants can be treated with a non-selective “brush killer” herbicide which kills or damages all treated plants. This herbicide application to suckers is probably best done when they are in full leaf and actively growing.

Finally, if you don’t want to use chemicals you can eventually kill the plant by continuing to cut the sprouts and suckers off. If you keep ahead of it, it will eventually exhaust its food reserves and die in much the same way as with girdling.