It's not just whether a given tree can "recover" from such poor pruning, it's what the long-term ramifications will be; All those stubs left all over the place will indeed likely have previously dormant buds "released" by the removal of the buds at the ends of the branches-the parts that are now gone. So far so good-the plant will appear to fill back out with live foliage. But the tree can't compartmentalize when branches are lopped off willy-nilly as seen here and consequently, there will very likely be a pocket of decay at the ends-or what are now the ends-of each branch so severely truncated. Even this might not matter so much if this is a species that matures at a low height, etc. It will be full of funky things but nobody will ever know that except for the OP and us readers, lol. But if this were a tall-growing species, having all that decay left up in the crown quickly becomes hazardous. Around here, the prime example of what I'm talking about are large, old silver maples, growing under wires, where the powerline clearance contractor has used less than stellar technique, leaving stubs behind. In each and every such case, regrowth of new sprouts has been explosive, but way back where the random cut was made, there is a well-defined pocket of decay, which can now travel down through the branch and even get into the main trunk. None of that might matter here if the OP keeps this tree small somehow. But that by no means should be used as an argument that this pruning was acceptable.

Well, so much for them being sick hemlocks! They are just mangy look cedars. (arborvitae) These are typical of plants that have been poorly maintained throughout their lives. The forking trunks are bound to cause problems sooner or later in a climate with periodic intense storms. You could remove them based on this, or not...but make sure you don't repeat the same mistake. Sheesh, can't we take a 1/2 day out of "common core" here and there and train young minds on the most basic, obvious aspects of horticulture? If you see a small conifer with a bifurcated trunk, fix it! The one on the left clearly had the problem when planted. Likewise, not every tree that sprouts is a magical gift from a deity that should be allowed to grow. etc. etc. I guess there are condos and not apartments, or you wouldn't care?

I would just remove the suckers from the bottom. Technically CMs are shrubs, so the mulch shouldn't cause too many problems. You could run a lawnmower over the mulch, and remove the adventitous roots, but this will likely create more suckers, making it more maintenance. See the link below for proper pruning. ==>>>http://thedailysouth.southernliving.com/2009/02/24/what-concerns-p/

the root flare needs to be at the surface ... without the application of a mulch volcano ... https://duckduckgo.com/?q=root+flare&t=ffcm&iax=images&ia=images https://duckduckgo.com/?q=mulch+volcano&t=ffcm&iax=images&ia=images tree trunks are not made.. to be buried .. basically.. they need to be dry.. not constantly moist by deep planting or the mulch ... so the first thing that needs to be done.. is to gently pull back the mulch.. and find out where the root flare is ... perhaps take some pix.. and bring them back here.. for more advice ... dead parts are dead.. and should be removed ... a tree saw and good ladder.. and a helper to hold the ladder ... should take care of the dead stuff ... once the dead parts are removed.. you should be pleasantly surprised how much better they look .... most likely they are severely stressed ... fert is not a response to such ... ken