Peel, pit and cut peaches in half. Cut one half into 8 slices and set aside. Roughly chop remaining halves. Add chopped peaches and lime juice to a food processor and purée. Strain purée for a smoother texture, if desired.
Divide purée evenly among 8 chilled cocktail glasses and top up glasses with ginger ale. Divide mint sprigs among glasses and garnish each glass with reserved lime zest strips and peach slices.