I live in LA where I been dealing with a well established mimosa next to my the house for several years. I adore plants, but this tree is a nuisance. Extremely invasive, robbing all the sunlight for other plants, so very messy and just not worth it's short flowering season or foliage.
Terribly sorry to hear that you see your Mimosa tree as a nuisance. I read elsewhere (but can't find the post) that Mimosa is messy.
I know little about the plant but have three at my place and they are not at all messy. I am falling in love with them.
I have been here in excess of a decade and never had a problem with them. Visitors adore them. So much so that some have obtained the Mimosa plant (Pink silk) for themselves.
The seeds are advertised as being that of a rare plant although I have no idea if this is true or not..?