In a sturdy glass or cocktail shaker, combine lime juice, mint leaves, and simple syrup. Muddle gently for about 30 seconds to release the mint’s aroma without tearing it into small bits.
Fill the glass with ice. Add grapefruit juice and top with ginger beer. Stir gently to combine.
Garnish with a lime wedge, mint sprig, or a thin grapefruit slice for a colorful touch. Serve immediately.