Anthracnose is a fungus that is promoted and spread by heavy rainfall (or irrigation) and dew.
Control is achieved by regular spraying of fungicides at the spray intervals recommended on the label. Spraying starts during flower panicle development and continues until the preharvest waiting period is reached.
To cut down on spraying consider planting Indo-Chinese/Philippine-type mangoes. Many of the mangoes in this group are relatively resistant to anthracnose and will significantly reduce dependence on regular spraying for disease control. The fruit have good flavor and low-fiber flesh (which is a good thing).
For more information about this disease see this UF/IFAS publication: http://edis.ifas.ufl.edu/vh048 To learn more about growing mango see this publication: http://edis.ifas.ufl.edu/mg216