I had a Siberian Elm right next to the side of my house and was able to kill it quite easily. Per instructions from somewhere online, I cut it down leaving a few inches of trunk above ground. Then put a tin can (without any lining) over the trunk, and pound it into the ground so as to keep out any sunlight. That was about 4 years ago. Once in a while I lift the can to take a peek, and not any sign of growth. As far as I know, the tree is dead, but I may be naive about what's going on with the roots. Hopefully they're going nowhere.