Add sugar and water to a medium saucepan. Heat over medium-high heat until the sugar dissolves. Add the ½ ounce of mint to the saucepan and bring to a boil. Reduce to a simmer and cook for 5 minutes. Remove from heat, cover, and let sit for 10 minutes.
Once the 10 minutes have passed, remove the mint leaves with a slotted spoon. Place mixture into medium bowl. Place cubed watermelon in pitcher for a blender. Place on blender and blend until smooth, about 1 minute. Measure out 2 cups of juice and add to mint syrup. Add lime juice and salt. Cover and place into refrigerator to chill completely, about 4 hours.
After the mixture has chilled, add chopped mint leaves. Freeze in ice cream machine according to manufacturer instructions. Note: because of all the sugar, the mixture will take a while to freeze. Mine took almost 20 minutes.
Transfer frozen mixture to storage container and freeze until firm, about 8 hours.