In a small saucepan over medium-high heat, bring the sugar and 1 cup water to boil. Cook, stirring, until the sugar is dissolved, about 10 minutes. Remove from the heat, add the mint leaves and allow to steep until cooled, about 15 minutes. Strain the simple syrup into a medium mixing bowl. Add the lemon juice, lemon zest, orange zest, lime zest, orange juice and 1/2 cup water. Stir to combine.
Pour the mixture into the frozen bowl of an ice cream maker and churn according to the manufacturer's instructions. Transfer the sorbet to a deep baking dish or loaf pan, cover tightly and place into the freezer until frozen, at least 4 hours and up to overnight.
To serve, scoop the sorbet into a bowl, drizzle with limoncello and garnish with a mint sprig.