Since no one has responded, I'll try. I'm guessing that you may have the straight species--Cotinus coggygria--with the blue gray leaves-- which has become increasingly hard to find in the trade. Years ago I would see many of these enormous shrubs in the Ithaca, NY area. The suckers will regrow but they are likely to get as large as the original.

You can prune it to keep it smaller by treating it as a cut back shrub--you well get huge growth each season but no "smoke" because it blooms on second year wood.

Perhaps you could take cuttings--I have no experience with or knowledge about Cotinus cuttings--and plant one of them elsewhere.

Some years back I really wanted the straight species but was never able to find a vendor.

these leaves are grayish maroon. i'll prune the suckers & see what i end up with.

Wear gloves when pruning them, they are related to both mangos and poison ivy, same family, so not deer-friendly! I do love them though.