1. First, make the grapes ice cubes: Place a few sliced grapes in ice cube molds and fill with sparkling grape juice. Freeze overnight or until ice cubes are solid.
2. In a large pitcher, combine lime juice and mint leaves and crush with a wooden spoon to muddle. Then add remaining grapes, sparkling grape juice (save a little for rim).
3. To serve, mix a little grape juice with granulated sugar. Rim cups with lime juice and then the grape sugar mixture. Place ice cubes in glasses, and then pour spritzer into glasses and garnish with limes and mint.