In a medium bowl, add sugar and mint leaves. Using a spoon, crush the mint leaves into the sugar and along the sides of the bowl.
Pour water, rum, lime juice, and thawed raspberry juice in the bowl. Stir together until sugar is dissolved.
Fill a pitcher (or a set of glasses) 1/2 way with ice. Pour in raspberry juice mixture, including crushed mint leaves. If pouring into individual glasses, fill each glass 1/2 way with raspberry juice mixture.
Slowly pour carbonated water down the side of the pitcher (or the glasses). Once filled, gently stir once or twice to combine.
Serve raspberry mojitos with raspberries and extra mint leaves as garnish.