Place the peaches, 1/4 cup of the water and 1 teaspoon of the lime juice in a blender or food processor and puree until smooth. Spoon or pour into ice cube trays, filling each cube only halfway.
Place the remaining water and lime juice along with the raspberries in the blender or food processor and puree until smooth. Spoon or pour on top of the peach mixture. Carefully transfer to the freezer. When solid, transfer to a large zip-top bag, label and freeze.