In a small saucepan, combine the sugar, water, and lime zest over medium heat. Bring to a simmer, stirring. Reduce the heat to low and stir until the sugar has dissolved completely. Remove from the heat and set aside to cool.
Put the frozen mango chunks in a food processor with the ice, wine, rose water, and the cooled lime syrup. Process for 2 to 3 minutes until the ice has broken down and the sorbet thickens. When done, the sorbet will have a slushy consistency. Transfer the food processor bowl to the freezer to harden the sorbet fully, about 1 hour. Store in a covered airtight container. Use within 1 month. To serve, spoon into martini glasses and garnish with mint.