Isn't there some paint/spray that will prevent the regrowth of the sucker shoots that you have removed? It is a never ending battle.
Certified GKH Gardening Expert
Cut the suckers and paint the fresh cuts with undiluted Round-up. This will get into the root system and kill the roots. It may take a month or so, but it will work. You can also try using a reciprocal saw to cut the roots out of the ground.