Put 1/3 cup raspberries, the cucumber, and 2 tbsp. mint in a pitcher. Add sugar. Mash with a wooden spoon or muddler until raspberries are crushed and mint is aromatic. Add lemon juice and gin and stir until sugar dissolves. Add seltzer to pitcher; gently stir.
Set ice cubes in 4 or 5 glasses (12-oz. size). Divide remaining raspberries among glasses. Pour in the cocktail and tuck a mint sprig into each glass.