Fill a tall glass with ice and set aside.
In a cocktail shaker filled with ice, add the grapefruit juice, lime juice, simple syrup, and tequila.
Shake vigorously until the mixture is well chilled.
Strain into the prepared glass.
Top with club soda and gently stir.
Garnish with a wedge of grapefruit and a sprig of mint. Serve immediately.