Just do not allow it to gain any top growth, cut the new shoots as
they appear (let them get a foot or so high to use up more stored
energy.
If any stands remain that are connected to the area you are trying to
clear you need to remove them or cut the rhizomes connecting the two
patches so it gets no food.
It just takes a bit of time to deplete any stored reserves and use up
the existing buds below ground.