In a small saucepan, combine the sugar and water. Heat over medium heat until the sugar dissolves completely, then remove from heat and let it cool to room temperature.
In a blender, add the strawberries, raspberries, and cherries. Blend until smooth.
Pour the blended fruit mixture through a fine mesh sieve into a large bowl to remove seeds and pulp.
Add the cooled sugar syrup, gin, and lemon juice to the fruit mixture. Stir well to combine.
Transfer the mixture to a shallow dish and freeze for about 2 hours, stirring every 30 minutes, until it reaches a sorbet-like consistency.
To serve, scoop the bloody sorbet into glasses over ice cubes.
Garnish each glass with fresh mint leaves and enjoy immediately.