Heat 4 cups of water in a pan for 2 to 3 minutes until hot. Add the tea bags and switch off the flame after 30 seconds. Remove the tea bags after 2 minutes and discard. Keep aside to cool.
Add 2 mint springs and cover. Keep it in the fridge for 3 to 4 hours. Puree the mango with 2 to 3 tblsp water (or more as required). Place this in the fridge for 2 hours.
To serve, remove the mint leaves from the tea and discard. Divide the mango puree among serving glasses. Add ice cubes, vodka and mint sprig. Top up with tea and serve at once.