I would not prune your mango anywhere near to a/the "stump" for a few reasons. One being, if there is a problem with the tree, severely pruning back will not cure the problem.
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Well, I cleaned the scale by hand, cleaned the sooty black stuff with a mild soap, applied copper to the leaves. About three months after I applied a Bayer systemic insecticide. The scale issue seems to have subsided. However, the tree appears to be stunned, it has not grown at all in over a year and some of the leaves are turning brown around the tips. Some of the branches are covered again in the black sooty dust. I will let it be til the end of spring, beginning of summer and then make a decision.