Divide the blackberries. Put 1 ½ cups into a mason jar.
In a saucepan, combine the remaining blackberries, water, and sugar. Heat the mixture on the stove on medium heat, while stirring occasionally.
When the syrup comes to a boil, decrease the heat to low and let it simmer for 10 minutes. While simmering, crush the blackberries in the saucepan with a masher.
Pour the syrup into the jar. Fill the top with grain alcohol. Secure the lid tightly. Shake the jar a few times and store it away from sunlight and heat sources. Let the mixture rest for at least three days. Remember to shake once or twice a day during the waiting period.
At the end of the waiting period, strain the liquid into another mason jar. Cover the lid and store it in the fridge.
For serving, place ice cubes in each glass. Put fresh blackberries over the cubes. Divide the cooled drink into serving glasses. Decorate each glass with fresh mint.