Bring 2 cups of water to a boil in a medium saucepan. Remove the pan from the heat and add the tea bags, mint leaves and half the cucumber slices. Cover and let steep until cool, about 15 minutes.
Meanwhile, combine the honey and 1/4 cup hot water in a measuring cup and stir until the honey is dissolved.
Fill a large glass pitcher with ice, 4 sprigs of mint and a few cucumber slices. Strain the cooled tea into the pitcher and discard the mint and cucumbers. Add the honey mixture and 4 cups of and stir to combine.
To serve, pour the tea into tall glasses full of ice. Garnish each glass with a few sprigs of mint and a couple slices of cucumber.