Rim a martini glass with sugar by running a lemon wedge along the rim and dipping it into sugar.
Fill a cocktail shaker with ice cubes.
Add vodka, mango puree, lemon juice, and simple syrup to the shaker.
Shake vigorously for about 15-20 seconds until chilled.
Strain into the prepared martini glass.
Garnish with a lemon twist or a slice of mango. Serve immediately.