Answer: In some cases a newly planted tree does not survive the winter, especially if it has been allowed to dry out during the fall months or if it was unduly stressed or poorly planted. Grafted trees may be more susceptible to stress. You might want to consult with the nursery where you purchased the plant to verify if there is a problem, or not, and since it was a bargain tree, if there is any warranty on it that might apply if there is a problem.
You should probably wait a little longer to see if any buds begin to swell. However, usually a lack of buds would indicate that the branch is dead. If you cut inside the branch and there is no green inside it, then that portion is dead and can be removed. If you suspect the branches are dead, start at the tip and snip a bit, working your way gradually up the branch to live wood. If the wood is dead, there is nothing you can do to bring it back.
On a grafted tree, removing all wood above/beyond the graft site would remove the special top portion of the tree, leaving only the root stock. If the entire top portion has died, then the tree will revert to whatever it was grafted onto.
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