Bring 6 cups of water to a boil. Remove from heat, add the white tea bags, and steep for 8–10 minutes. Squeeze the tea bags well, discard them, and let the tea cool completely.
Add the fresh raspberries to a blender with 1 cup water, lemon juice, and honey. Blend until completely smooth.
In a large pitcher, stir together the cooled white tea and the raspberry puree until evenly combined.
Add the clapped (not muddled) mint leaves to the pitcher. Refrigerate and let infuse for 10–15 minutes, then remove and discard the mint to prevent bitterness.
Continue chilling the tea until fully cold, about 1–2 hours.
Fill glasses with ice. Pour over the chilled raspberry mint iced tea and garnish with fresh raspberries and mint leaves.