hard to tell for sure from the photo, but a few of the upper leaves look like they're lobed, so what you might have is a crabapple. If the shoots are growing from the rootstock (below the graft), they won't be the same as the original tree.

We had a liquid amber removed, and it's roots have sent shoots up every where. Roots go out as far as the tree canopy and even farther! We finally bought concentrated round up, and mixed it strong. Took a year to get the thing to die!

We had the stump ground out when it was removed, and a fig tree is now happily growing in it's place.

I'd get rid of the suckers and plant something productive and beautiful in it's place.

SnailLover, the decision to leave or remove is within you.

Decide:
-Is that neat red and green color looks interesting enough
-Is the new growth the cherry tree or the rootstock
-Is the rootstock is anything desirable. That will tell you what shape it will "want to" grow in. I had a Nyssa sylvatica Wildfire die back and when it started to resprout I would have been 99% as happy with a regular Nyssa not the cultivar so I let it go.
-Do you have the patients to let it go a few years and try to prune or let it take whatever shape?

Out in my back yard I would leave it for sure. It looks interesting. If it was someplace I thought needed a particular shaped tree I might try to dig it up and move it to the back even thought transplanting an established shrub is more trouble than it is really worth.

Named varieties of trees are seldom grown on their own roots. They are grafted on to rootstocks. This is to ensure that the exact variety is being sold and also because very often the variety has week roots that may not sustain the plant. The rootstocks are usually of the same species but are selected for their strong root growth or other desired trait. As your ornamental graft got sick and died the rootstock survived and took over. The rootstock will not be as ornamental as the variety. It will probably have the usual white cherry blossoms and will probably produce fruit that will have little value, except as bird food. It may also put out sucker a good distance from the original tree. Three years ago, we moved into our current house. There was a large, mature Shirofugan cherry in the front yard. Since the tree had only gotten natural watering for a couple years, the rootstock had sent out runners to maximize its water gathering capacity. Then the roots produced suckers. These showed up more than 10 feet beyond the drip line of the original tree. They made the lawn unusable and unsightly. This year I cut the tree down and gave the wood to a woodworker. Cherry is a beautiful wood. I am taking care of the sprouts with Knockout and have replaced the Cherry with an Emerald City tulip tree.

After all that, if you are curious, let grow for a few seasons. At least you'll know what the rootstock tree look like.

In case anyone wants to know, the active ingredient in Knockout is glyphosate.

When it comes to woody plants, triclopyr is more effective than glyphosate.

A tip for those thinking about cutting down a tree that will send up numerous suckers later on -- as soon as the tree is cut down, paint the outer two inches of the cut surface with a product containing triclopyr.

Another tip:
If sprouts are arsing from a previously cut down tree, as you cut the sprouts, immediately paint the cut surface of the stump with triclopyr.

This post was edited by jean001a on Sat, Aug 2, 14 at 13:36

Thanks everyone for the helpful info. I think arbordave is right that it may be a crabapple. I do remember now that it had little clusters of something on it. I just moved in last year, and I was too busy with the other problems to pay much attention to it. Since it is in a prime location by the driveway, I think I'll try digging it out and put it in the back yard where my other rescues & rejects live. Then I'll put something nice in its place.