Rinse the blackberries under cold water to remove any dirt. Pat the berries dry with a paper towel.
Combine the blackberries, sugar, and water in a saucepan. If using fresh mint, add a few sprigs to the pan as well.
Place the pan over medium heat and bring to a gentle simmer. Stir the mixture occasionally to help dissolve the sugar and keep the blackberries from sticking to the bottom of the pan.
Let the mixture simmer for about 10 to 15 minutes or until the blackberries soften.
Remove from heat and allow the blackberry juice mixture to cool slightly.
Strain the juice into a container using a strainer, pressing down on the blackberries to extract as much juice as possible. Discard the leftover pulp and seeds. Remove the mint sprigs as well.
Taste and adjust the sweetness of the blackberry juice as needed. If you add more sugar, stir the juice well to dissolve it completely.
Cover the container and refrigerate the fresh blackberry juice until chilled. You can also serve it immediately over ice.