Cut the shoots close to the base of the tree by snipping them with loppers about a half inch from the trunk. Don't nick the trunk.
Push soil and leaves back from the cut area so any potential diseases lurking in the ground cover won't contact the fresh wounds. You can push it back in place after a week.
Dip a brush in sucker growth inhibitor. This is a formula designed to slow or stop suckers from forming.
Brush the cuts of the tree with the inhibitor, coating thoroughly. Reapply a week later.