Puree the cucumber and mint leaves in a blender until juicy and chunky. Set aside.
In a small skillet, heat the coconut oil and olive oil over medium heat until the coconut has completely melted. Immediately pour into a medium bowl. Add the sugar and cucumber-mint mixture and stir until combined.
Divide the sugar scrub between four half-pint mason jars. Secure with lids and store in the refrigerator.
Scrub 1 teaspoon over your face daily in a circular motion for 60 seconds. Rinse with water when finished. Keep scrub in fridge until use.