Makes about 7 1/2 cups
Combine blackberries and sugar in large container. Crush blackberries with wooden spoon. Add mint and baking soda. Set aside.
Pour 4 cups boiling water over tea bags; cover and let stand 3 minutes. Discard tea bags.
Pour tea over blackberry mixture; let stand at room temperature 1 hour. Pour tea through a wire-mesh strainer into a large pitcher, discarding solids. Add 2 1/2 cups cold water, stirring until sugar dissolves. Cover and chill until ready to serve. Garnish, if desired.