Did this thread lose some posts? I thought someone confirmed it was Black Cherry. iKandy, Prunus serotina may not be the most ornamental cherry but it is still a wonderful naive tree because it is an excellent wildlife tree and it is also prized for its wood which produces cherry cabinets and furniture. The birds love the fruits and it is a host plant for some of the most beautiful butterflies and moths, such as the Eastern Tiger Swallowtail and the Promethea moth. For me, Black Cherries and Choke Cherries are not generally ornamental enough to grow in a highly visible position in the landscape, such as the front yard, but I have many of them in the back yard where the landscape is more naturalized and love them. So if you are okay with where it is, leave it. As for all the shoots, they are probably either suckers or water sprouts, and I would prune off whatever extra shoots you don't want, as well as thin out any dead, crossing, or duplicate branches.

Possibly, if they are growing from the roots and not the trunk, and you got some of the roots, you might be able to pot them up and grow them on to plant out in the fall. It does look as though the further-out sprouts are coming up from roots. I would think you would have better luck potting them than planting them directly in the ground, as you can pay better attention to watering a pot, especially on in part-shade, than you can to a somewhat fragile baby in the ground. One reason you may be getting sprouts is that it looks as though the mulch is too deep, certainly too deep right next to the trunk. There should be a minimum of mulch (best is none) right next to the trunk, and the root flare, where the roots grow out from the trunk and the trunk gets thicker, should be visible at ground level - the tree should not look like a telephone pole where it meets the ground. While you are digging down to the origins of the sprouts, you might pull back and possibly thin out the mulch at the same time. The mulch in all areas under the tree should be no deeper than 4". In any case, try to get down to the very base of where the sprouts are growing from, whether root or trunk, and pull them off rather than just cutting them - they WILL resprout in abundance from being cut, but might not from being pulled off - if they do, it would be in ones or twos, not multiples.

Google for choke cherry, maybe adding "drawbacks" to the header, and see what you get. Looking at the normal growth characteristics may give you some facts you can use as well. Suggesting you will replace it with another tree (or several trees) more to your liking, that will serve the same purpose as feeding the birds, may help. Do check your choice(s) against the invasive tree lists, as some trees that wildlife really like are invasive - one reason being BECAUSE the wildlife like them, and spread the seeds far and wide!

You want to remove that as it will just be a wild cherry stem from the rootstock. Cut it off as cleanly as you can from the root, and cover the root with just a little extra soil - that might discourage further suckers, but don't cover it too deeply, just 5cm or so. Resin PS spellcheck: 'Kanzan' (the w is a common nurseryman's error)