Q: A stump carver made this statue out of the stump of a water oak that we removed in November in our back yard. In spring, branches started to grow.
A: Water oak has many shallow buds under the bark, which sprout readily when the tree is stressed. When you removed the top of the tree, the stump that was left tried to form new foliage.
I think the best thing to do now is to clip off the sprouts at their base, next to the bark.
My prediction for the future is that the bark will gradually slough off. You will need to protect the newly exposed wood with varnish or polyurethane or whatever your carver recommends.
It is particularly important to protect the top of the stump so rainwater does not infiltrate from above. You’ll need frequent applications of protectant to accomplish that.