Answer: Mimosas may suffer some dieback during the winter (due to excessive cold and/or breakage due to storm damage) so that some of the branches do not leaf out the next spring. These dead portions should be trimmed off once you are sure they will not leaf out and broken branches should be neatly removed. New buds sprouting along the trunk can be rubbed off while still very small. Sometimes, excessive top dieback will result in new stems growing from the roots. This will develop into a multi-stemmed tree, mimosas are often multistemmed. These trees are potentially subject to so many pest and disease problems that it is better to avoid pruning as much as you can -- each cut opens the bark and provides a possible point of entry. If your tree is grafted however you will want to remove any new growth that originates below the graft as soon as you see it. If you do not do this it will be more vigorous than the grafted top and will overwhelm it. If you are not certain how to proceed I would suggest you consult on site with a professionally trained and certified arborist. It is just so difficult to make pruning recommendations long distance. Good luck with your tree.
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