1. Combine blackberries and sugar in a large container, and crush with a wooden spoon; stir in mint and baking soda.
2. Pour 4 cups boiling water over tea bags; cover and steep 5 minutes. Discard tea bags.
3. 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 1 hour. Garnish, if desired.