Muddle blackberries, cucumber, and mint in the smaller half of a cocktail shaker. Add vodka, lemon juice, and simple syrup and fill with ice. Shake until well chilled, about 12 seconds. Double-strain into an ice-filled collins glass, pour the ginger beer down the side of the glass, and give it a brief, gentle stir. Garnish with mint sprig and cucumber wheel, plus a straw if you have one.