It is not impossible to get rid of Japanese knotweed. True, this aggressive-growing perennial weed is considered one of the worst invasive weeds wherever it is found. But with consistent monitoring and the application of a variety of control methods, it can be eradicated. But be prepared for the long haul---you will likely have to combat Japanese knotweed for several seasons before it finally gives up its foothold in your yard.
Dig up individual shrubs. Use a shovel or trowel to dig up all of the Japanese knotweed's roots. If even a small piece is left behind, it can grow into a new plant—or several. Once you think you have removed all of the roots, expand the hole by a few inches on all sides (as long as there are no desirable plant roots in the way), including the bottom. Sift through the dirt with your fingers and remove any pieces that you find. Continue to expand the hole until you stop encountering small root pieces.
Cut the Japanese knotweed back to ground level. Do not allow re-growth to reach more than 3 inches in height. By repeatedly removing the Japanese knotweed's foliage, you will eventually starve its roots to death and it will produce no more plant material. This method is best for Japanese knotweed growing amongst desirable plants that may be harmed by digging or herbicide spray. For this method to be effective, you will have to cut the knotweed back several times a year for several seasons.
Apply a glyphosate herbicide to the knotweed. Use an individual spray bottle to coat each knotweed plant's foliage with the herbicide according to the manufacturer's instructions. Take care not to accidentally spray non-target plants. Glyphosate will kill anything it touches. You may paint the foliage of young knotweed plants by dipping a small paintbrush in the herbicide and coating all of the foliage. The best time to treat knotweed with herbicide is during the active growing season. Re-spray the plants as necessary at the intervals dictated by the herbicide's manufacturer.
Monitor your yard for re-growth. The above control methods must be applied season after season to any new growth or the stand will re-establish itself. If at all possible, kill any new growth before it reaches over 3 inches in heights, or its root system may become strong enough to produce new growth.