Pound a couple copper nails into the trunk.
L
If you cut the tree and treat the inner bark with a very concentrated treatment of glyphosate, it will go into the roots and kill the roots.
Same treatment for tree of heaven.
Tree of Heaven (Ailanthus altissima) - Identification & Control (without causing it to sucker!)
https://www.youtube.com/watch?v=hHsSCn6L450