In a small saucepan, bring the cranberry juice, 1/4 cup sugar and orange peel to a boil. Cook and stir until sugar is dissolved. Remove from the heat; stir in ginger.
Place remaining sugar in a small bowl. Remove orange peel from syrup; add to sugar, one piece at a time, and shake to coat. Place in a single layer on a foil-lined plate. Let stand overnight. Cover remaining sugar; set aside.
Transfer cranberry mixture to a 1-qt. dish; cool to room temperature. Freeze for 1 hour; stir with a fork. Freeze 2-3 hours longer or until completely frozen, stirring every 30 minutes. Stir granita with a fork just before serving; spoon into dessert dishes.
Lightly moisten mint with cold water; dip in remaining sugar to coat. Garnish granita with mint and candied orange peel.