Place about 4 raspberries in each compartment of an ice cube tray, 6 hours before serving iced tea. Fill with water and freeze.
Place honey, 2 cups water and ginger in a saucepan and bring to a boil. Reduce heat and simmer over low heat for 5 minutes. Remove from heat and add tea bags. Let mixture steep for at least 30 minutes and up to 1 hour, then strain out solids.
In a pitcher combine strained liquid with 6 cups water and lemon juice. Chill in refrigerator.
To serve, place 3 ice cubes in a tall glass and pour iced tea over cubes. Garnish with lemon slices and mint sprigs.