For the juice mixture: Place the apple, carrot, orange and pomegranate juices into a jug and mix well to combine. Stir in the grated celery and ginger and chill until serving.
For the cocktail: Place crushed ice into 4 glasses and pour a shot of vodka into each. Wrap an orange slice around each celery stick and place in the glass together with a few mint leaves. Top with the juice mixture and serve.