Combine the sugar with 1/2 cup water in a small saucepan. Heat together, stirring, until the sugar dissolves, then turn off the heat and let cool completely.
Slice half of the blood orange into wheels. Reserve 2 wheels for garnish. Muddle the remaining orange wheels with 1 sprig mint and 1/2 ounce simple syrup in a glass shaker (save the remainder for another use). Juice the remaining half of the orange, adding the juice to the shaker. Add the sherry and shake. Strain into a highball glass filled to the top with ice. Garnish with the remaining mint and the wheels of blood orange.