One of the reasons Tree of Heaven is such a menace is the fact that it is rhizomatous and suckers aggressively.
If you decide the cut it down, you'll probably need to treat the stumps with herbicide. If you cut it off and don't treat it, you'll just make it mad and there will be several replacements next year.
If you really don't want to use herbicides, the tree appears small enough that you might be able to get rid of it by digging the entire root system, but I wouldn't bet on it (it may be just be a sucker attached to a nearby large tree).
