Combine 4 cups water and sago pearls in a saucepan; bring to a boil. Cook and stir for about 3 minutes, remove saucepan from heat. Cover and let stand until sago pearls are semi-transparent, 2 to 3 minutes.
Drain hot water from sago pearls in a strainer and rinse under cold running water until water runs clear.
Blend 2 cups water, mangoes, evaporated milk, and sugar in a blender until thick and smooth; pour into a bowl and stir in sago pearls. Refrigerate until chilled, at least 30 minutes.