Sounds like you got a grasp of the weed known as mimosa. That single arching stem will leaf out and just cutting won't kill it. If instant results are wanted you need to grub out the root. Continued cutting will eventually kill the root however. Fortunately, mimosa is extremely sensitive and glyphosphate will burn it to the ground.
As to it's form, it is what it is and no amount of pruning will make it what it isn't.

They are pretty late to leaf out - early May in the area north of Atlanta. You can scratch the bark to determine if they are still alive. If it is green, it is alive and will put leaves out.

But please, kill every one that you can ... what a pest. Except for 3-4 weeks of pretty flowers, it's not a great tree: late to leaf out, no fall color, seedlings everywhere. And no support for wildlife except for nectar on the flowers. By contrast, native trees provide nectar, foliage for caterpillars (which is baby bird food), and fruit/nuts for wildlife.

I have repeatedly tried to kill one that came up in the iron fence...Roundup didn't phase it...chopping it down doesn't work either. Yes they are very pretty and fragrant while blooming, but a very messy tree.

I've been daily killing a mimosa tree in our CL fence for years. I mean I rub all of the foliage off almost daily and it will not die. I keep it covered in leaves and debris to block the light, sometimes chop at it with a shovel. I've already found foliage growing again this year. This summer will be my 4th summer of trying to kill this thing manually. It's not possible to dig it out, it's IN the fence. There is nothing you can do to alter the shape of this giant weed.

I don't know which I detest more--English Ivy or mimosa. I do know I've never met anyone down here who cultivates them--even on Mimosa Dr. (there really is such a place) in Decatur.

Best Wishes--Carl
Atlanta, GA

I pulled up one of the ones in my garden bed and the 8 ft it grew that shocked me was nothing compared to the 12+ft of root it had going everywhere. I have 3 more to get out of garden beds that are right up at the house foundation.

Question though, how does someone get one like this?

if i was their neighbor i would hate them. but still, theirs looks like a tree. mine look weird.

Here is a link that might be useful:

I love mimisa. mine looks like the one in the pic
in post above. my only regret is that I should
have planted it in the front yard!

I've had no problems with it being invasive at all.
or any in the many houses I lived in growing up
with mimosa.