Combine raspberries and grape juice in container of an electric blender; cover and process until smooth, stopping once to scrape down sides. Strain mixture through several layers of dampened cheesecloth, reserving liquid and discarding solids.
Combine reserved liquid, sherbet, water and lemon juice in blender container; cover and process until smooth. Add ice cubes; cover and process until frothy. Serve immediately. Garnish with fresh mint sprigs, if desired.