In a saucepan put water, stevia, 1 tbsp zest from the lime and all the juice from the lime to a boil. Stir occasionally, add half the mint and continue to let boil about 5 minutes. Remove from heat and let cool slightly. Then move sweetened mint-lime water to refrigerator to chill further.
In a medium pitcher or two serving glasses add remaining mint & cucumber slices.
When mint-lime water is cooled, add ice to the pitcher (or glasses) and add sweetened water. Add remaining cold water to dilute the mixture. Serve.