Place raspberries in a blender; process until smooth. Pour raspberry puree through a wire-mesh strainer into a bowl, discarding pulp and seeds remaining in strainer. Return strained puree to blender. Add sliced banana and 1 can juice concentrate; process until smooth.
Pour mixture into a large freezer-proof container. Stir in remaining 1 can juice concentrate and 2 cups water. Cover and freeze 4 hours or until slushy.
To serve, transfer juice mixture to a small punch bowl. Stir in mineral water, and serve immediately.