Combine sugar and 2 cups water in a small saucepan. Bring to a boil, stirring, until sugar is dissolved, about 1 minute. Let stand until room temperature, about 30 minutes.
Bring a large pot of water to a boil. Prepare an ice-water bath. Plunge mint into boiling water for 10 seconds. Transfer mint to ice-water bath until cool.
Squeeze excess water from mint, and transfer to a blender. Add sugar syrup and vitamin C. Puree until smooth. Strain through a fine-mesh sieve. Transfer to a covered container, and freeze until solid, at least 4 hours.