Those are chokecherry suckers, they come from the roots. If you want a single chokecherry tree, you should pull them out. Expect to pull them out every year, chokecherries spread from their roots and will form large colonies if you let them.

If I pull them out and replant them somewhere else would a new tree grow?

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.