Bring a large pot with 12 cups of water to a boil over medium heat. Add the tea bags and let them steep for 10 minutes. Allow the tea to cool and discard the tea bags. Pour the liquid into a large glass pitcher.
Meanwhile, add the sugar and 1 cup water to a saucepan and bring to a simmer, over medium heat, stirring to dissolve the sugar. Drop in the handful of mint, remove from heat and allow the mixture to cool. At this point, strain and add the sugar syrup to the pitcher. Stir the drink well and divide it between 12 glasses filled with ice. Garnish each serving with some fresh mint sprigs and raspberries.