Knotweed is a perennial, bush-like plant that is often planted as an ornamental hedge because of its striking foliage and attractive greenish white flowers. While suited for landscape use, knotweed becomes problematic when left untended for a period of time. When left to its own devices, knotweed is an aggressive grower. But because it reproduces through deep underground rhizomes as well as seeds, it cannot be killed by just cutting it back before the flowers produce seed. Knotweed is also resistant to most broad-leaf herbicides. Only aggressive and repeated culling over one or more seasons can dispose of knotweed for good.
Use lopping shears to cut the stand of knotweed back to the ground.
Use a shovel to overturn the soil in the knotweed bed (watering the bed the night before will make the soil easier to work). Remove all of the rhizomes and rhizome pieces that you unearth. If the patch is small, you may consider removing the upturned soil and replacing it to eliminate any seeds that may be lurking in the soil.
Spray any knotweed shoots that sprout up with a glyphosate broad-spectrum herbicide like Round-up once they reach 6 inches in height. This herbicide will kill anything that it touches, so use a small handheld sprayer and spray each plant individually. Spray on a windless day and cover all of the knotweed's tissue, including the underside of any leaves. Re-spray at the intervals specified by the manufacturer.
Re-plant the area next season. A ground cover that grows competitively in your area will be able to out compete any subsequent outcroppings of knotweed.