Cut the plant off between 2 and 4 inches above the ground.
Slide a long, strong wire down the hollow stem and pierce several stem segments.
Use Round-up (available at local garden supply centers) and spray your fresh cut and in the hollow stem with Round-up. Be sure to follow all instructions and precautions on the container label.
Do not dispose of in regular organics or compost!
The knotweed will regrow within a couple of months. Once regrowth hits about ¾” in diameter, follow the same procedure as above. Continue until regrowth stops.
If you are not comfortable with this method, please hire a local landscape contractor to assist you.
An attempt to dig out Knotweed will loosen up the soil and that allows it to regrow stronger and become more established. It will regrow from any missed piece of root. In the end, it will require more herbicide to eliminate it.