In a small saucepan, combine the wine or water and sugar.Heat on low until sugar has dissolved. Pour into a shallow pan and let cool.
Add blood orange juice to the sugar syrup and mix to combine.Place in the freezer. After 1 hour, break up ice crystals by stirring with a fork. Continue to check every hour until all the mixture crystalized, approximately 3 hours.
To serve, scoop into chilled serving dishes, garnish with mint and serve immediately.