1. Puree half the mango, strawberries, banana, and 1/2 cup pineapple juice in blender. Pour mixture into a container with a tight-fitting lid. Repeat with remaining fruit and 1/2 cup juice. Cover and freeze puree until firm, 5 hours.
2. Let puree stand at room temperature 10 to 15 minutes, until slightly softened.
3. Chop 1 cup of ice in blender. Add 1 container of fruit puree and 1/4 cup pineapple juice. Blend on medium-high until smooth. Pour into serving glasses. Repeat. Makes 8 cups.