Combine apple juice, ginger beer and mint in a large jug. Chill until ready to serve.
Just before serving, roll the pomegranate on the bench to loosen the seeds. Score around the middle and tear open into halves. Hold each pomegranate half over a bowl, seeds facing down and tap the skin with a wooden spoon, squeezing a little to release the seeds and juice. Remove any white pith then add seeds and juice to the punch with the mango, blueberries and peaches.