We dug down almost THREE FEET all along the front side of our house and extracted every root we could find. We spent over a week trying to remove it all. Next year? It all came back as if we'd never done a thing.
the only reason my mint-mint (i think it's spear, but honestly i've forgotten) isn't a horrible spreader though is because the hideous day star keeps it in check. it would adore to fill the entire yard if it weren't too hot for it.