Place strawberries and raspberries in a blender or food processor; process 30 seconds or until smooth, stopping once to scrape down sides.
Pour fruit mixture into a wire-mesh strainer; press with the back of a spoon against sides of strainer to squeeze out juice. Discard pulp and seeds remaining in strainer.
Combine fruit juice, grape juice, and sweetener; stir well.
Pour mixture into an 8-inch square baking pan. Cover and freeze until mixture is almost firm.
Break frozen mixture into large pieces, and place in blender or food processor; process until fluffy but not thawed.
