I know of many uses for mango and parts of the tree (eg, tea, tinctures, seed powder, root paste, roasted fruit...), but nothing includes consuming fresh leaves.
May
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Mangos can irritate humans as they are in the same family as poison oak, the anacardiaceae. Sometimes known as "mango mouth." Apparently the affected human can experience the same inflammatory response as the meal exits, so to speak.
Torts can eat poison oak leaves, and they do according to The Behler info on radiateds. I can't imagine thick mango leaves are that palatable, but if they like them, why not. I believe that traditionally mango leaves have been fed to cattle in times of drought and poor hay crops in India.