Don't start cutting anything off of the tree yet, those are helping create energy for the plant. And the tree still has roots in the ground even if it is impaired so you shouldn't need a cord to hold it up. Howard doesn't recommend them very often, especially for established trees.
It looks like a tree that came with the house - was it put in by a builder? Chances are a tree from a black pot is both too deep and the roots are still growing in the small shape molded by the pot. A recently planted tree could be dug up and the roots straightened out before replacement. If it has been a while, you have to pamper it a bit and remove any circling/girdling roots.
Check to be sure the tree wasn't planted too deep in the ground; the flare should be exposed. Since the view of the flare on your tree is blocked by leaves you'll have to check. Here is information about doing it by hand:
https://www.dirtdoctor.com/garden/Flare-Exposure-by-Hand_vq13018.htmInsects attack a tree that is already in stress, so these may be one of the causes. Because of the stress and damage, you will have to take some steps to help the tree recover. Have you heard of the "sick tree treatment"? This is a time when it can really make a difference.
Sick tree treatment.
Make sure the tree is properly planted regarding the flare then try the sick tree treatment. Leave the suckers (what you called "baby trees") and extra leaves for the time being.