Spear three cranberries alternately with two mint leaves on each wooden skewer. Place skewers on a baking sheet; cover with damp paper towels, and refrigerate up to one hour.
In a large punch bowl, stir together fruit juices. Fill the glasses with ice, and ladle about 1/2 cup punch into each glass; top with sparkling wine. Garnish each glass with a swizzle stick.
Use a citrus reamer, juicer, or press to extract the pomegranate juice; strain liquid through a fine sieve set over a bowl, and discard solids.