I have no ability to ID the exact problem and frankly I doubt many could from a picture. In mangoes my thoughts always go to fungal infection. Spraying with copper topically can help. With some sever fungal infections, systemic fungicides may be more effective but less desirable because it is a fruit producing tree. Of course, at this stage you won't be interested in eating fruit, just saving the tree. I frankly never use systemics, but there is relatively low risk as far as I know if you are not going to be eating fruit any time soon. If it isn't a fungal problem then it is a viral or bacterial problem. I have never treated for either of these. I would cut off the affected portions, give the tree good hydration and some weak or time released fertilizer and see if the tree out grows the problem. If not, I would replace the tree.