Cut the entire plant down to ground level. Use a hedge clippers and remove all of the leaves. There should be only stubs barely rising above the surface of the soil.
Cover the stubs of the plant with several layers of cardboard. The more humid and the more rainfall you get in your area, the more layers of cardboard you need to put down, because rain and humidity cause cardboard to break down fast. The idea is to completely smother the roots of the plant and not allow any light to reach them.
Secure the edges of the cardboard to the ground with rocks or bricks at the corners. This will help keep it from blowing away.
Cover the cardboard with a 4- to 6-inch layer of organic mulch, such as wood chips, shredded bark, straw or hay. The mulch will also protect the cardboard somewhat from the elements, helping it to last a bit longer before it decays away.
Leave the cardboard and mulch in place for at least 12 months. Check the area periodically. If the mulch appears to be decaying, apply more to bring its depth back to 4 to 6 inches. If the cardboard is decaying, push the mulch aside, remove the cardboard and replace it with an equal number of layers of fresh cardboard. Replace the mulch, ensuring it is at least 4 inches deep.