Add orange juice, pineapple juice, lime juice, and mint leaves to cocktail shaker, then fill with ice.
Shake mixture until just combined and chilled, about 5 seconds.
Strain cocktail into chilled collins glass or hurricane glass half-filled with crushed ice.
Top with additional ice, then pour grenadine over top, allowing it to settle to bottom of glass.
Garnish with mint sprig and serve.
