I have several large thornless honey locust trees in my yard and have always had trouble with them coming up off the roots, what can I use on them after cutting them off that will not affect the large trees but will kill out the shoots, I would like to kill the large trees but they are all I have.

Larry-
They are attached to the tree, whatever you do to kill them will affect the parent tree. This is a common problem with Locust. I have them all over my pasture and just keep cutting them.
Tony M