Place the orange and lemon zest, honey, sugar, mint, and water in a small pot over low heat. Cover and cook until the sugar is dissolved. Take off the heat and let cool to room temperature.
Add the juices from the blood oranges, orange, and lemon to the bowl with the sugar syrup. Strain entire mixture through a fine mesh sieve into a large mixing bowl. Discard the solids.
Place sorbet base into an ice cream machine and churn according to manufacturer’s instructions. Serve immediately or freeze. Makes 3-4 cups.