Place 2 cups raspberries in a wire-mesh strainer; press with back of spoon against the sides of the strainer to squeeze out juice. Discard pulp and seeds remaining in strainer.
Combine raspberry juice, strawberries, and sugar in container of an electric blender; cover and process until smooth, stopping once to scrape down sides. Combine fruit puree and white grape juice; stir well.
Pour mixture into freezer container of a 2-quart hand-turned or electric freezer. Freeze according to manufacturer's instructions. Pack freezer with additional ice and rock salt, and let stand 1 hour before serving. If desired, garnish with fresh raspberries and mint sprigs.