Heat sugar and water and dissolve over low heat to in a small pan while stirring, then cook over medium heat for 4 minutes. Allow syrup to cool. Add mineral water with grappa, prosecco, 1 teaspoon lime juice and 1/3 syrup, mix well, pour into a small metal bowl and set for 5 hours in the freezer. Puree raspberries and pour through a sieve.
Mix residual syrup and lime juice, also fill in a metal bowl and freeze for 5 hours. Shake up both sorbets with a knife until loose. With a spoon, scoop one sorbet on top of the other in a bowl. Briefly put again in the deep freezer. With an ice cream scoop, distribute on plates. Garnish with extra raspberries and mint leaves.