Bring 1 cup of sugar and 1 cup of water to a boil in a saucepan over medium-high heat, stirring to dissolve the sugar.
Add 1/2 cup of fresh, chopped ginger. Remove from heat, and let steep 30 minutes.
Pour syrup through a fine sieve into a heat resistant container; discard ginger. Chill in the refrigerator. If you made extra, just store it in an airtight container for up to a week.
Sangria:
Thinly slice 3 tangerines and add them to a pitcher.
Add 1/3 cup of fresh mint leaves to a glass with barely enough sake to cover and mull them.
Add the mulled mint and the remaining sake to the pitcher.
Add the chilled ginger syrup to the pitcher and mix well. You can add extra mint to look pretty.
For each glass wipe the rim of the glass with a tangerine slice and then twist the wet rimmed glass in the sugar.
Add sangria to glass and garnish with tangerine slice and mint.