Place the mango, sugar and water in a blender and puree. Pour into a pot, bring to a simmer, and simmer 2 minutes to dissolve the sugar.
Set a fine sieve over a tall, narrow bowl. Strain the mango mixture, in batches, through the sieve, using a whisk to stir and push as much juice out of the pulp as you can. Pour the strained mango mixture into a serving vessel. Mix in the lime juice and pineapple, orange and banana juice. Refrigerate this tropical mango limeade until well chilled (can be made several hours before needed).
When ready to serve, fill glasses with ice. Give the tropical mango limeade a stir, pour into the glasses, garnish each glass with a half lime slice, and enjoy.
Note: This drink is fairly tangy. If you like things sweeter, increase the amount of sugar used. Pineapple, orange and banana juice is available in the boxed and bottled juice aisle.