Don't cut it! Killing it that way, although possible, takes
many years, and you risk spreading it, as Dan says.
Spray it with glyphosate (Round-up). I think the very best time to do that is the autumn after it's flowered, because you can poison a lot of leaves that way, just as the plant is sucking down the goodness preparing for winter. But in the spring is good too. You will need to do this for at least three years, probably. I'm on year 2, and the evil weed is certainly looking nervous now.
See the Japanese Knotweed Alliance website for more information.