How do I kill a mulberry bush/tree once and for all?

They are a mess around here. Grow everywhere! At least they are easy to cut. I use the loppers to the sprigs off. When they are small 1/4 inch or so the weed trimmer will cut them but they seem to grow to an inch over night. When they get to big for the weed trimmer I just cut them off and toss them in the yard and let the riding lawnmower deal with them. Anything over ... say an 1 1/2 I'll cut with the chain saw into little logs and burn them in the chimmenia (sp). Those things can burn a large brush pile up pretty fast. Makes a good beer drinking project with buddies that come over. I think they used to call them incinerators but now it's a decorative functional yard ornament? Put some hail screen over the top so you don't set the neighbor's house on fire and have hot dogs and clothes hangers ready in case the firetrucks show up.