Japanese Knot Weed

I live on the banks of the Columbia River in Astoria, and there are two clumps of Japanese Knot weed trying to take hold. I understand that it is quite invasive, so want to get a handle on it. I was going to clip it down, and put the brush in the garbage can - not compost recycling. I do not want to put some horrible weed killer on the roots - do you have a recommendation? Thank you very much.