Mimosas (also called, "silk trees") can be real pests in the landscape. A frustrated reader recently asked About's Forestry Guide, Steve Nix a question on getting rid of mimosas. Steve, in turn, posted the question in his forum, where a very detailed method for getting rid of mimosas was provided. It's worth having a look at, even if your problem is not getting rid of mimosas, specifically, but some other invasive plant.
While I sympathize with the reader's plight, I can't help but think that mimosas at least have one major redeeming quality: namely, that the mature trees are quite attractive. It's far worse to have to lock horns against a stubborn invasive plant that has little to recommend it, such as Japanese knotweed (see photo). This tall perennial weed leaves behind ugly dead canes that litter the landscape every autumn!
Photo ©2005 David Beaulieu (licensed to About, Inc.)