In a small pot, combine mashed blackberries, lemon juice, and stevia. Heat over medium heat until juices begin to separate and bubble creating a syrup, about 5 minutes, then remove from heat. Allow to cool about 15 minutes.
In a small bowl combine cooled blackberry syrup, mint leaves, lime juice, mash with a muddler.
In a shaker combine mint/blackberry mixture, carbonated water, rum, and ice. Shake until well combined.
Pour into a glass and garnish with whole blackberries. Enjoy responsibly!