In a small saucepan, combine 0.5 cup of blackberries with simple syrup. Heat gently over medium-low heat, stirring occasionally, until the blackberries have softened and released their juices, about 5-7 minutes. Mash the berries slightly with a fork.
Strain the blackberry syrup through a fine-mesh sieve into a bowl, pressing on the solids to extract as much liquid as possible. Discard the solids. Let the syrup cool.
In a pitcher, combine the cooled blackberry syrup, fresh lemon juice, and remaining 0.5 cup of blackberries.
Fill glasses with ice cubes.
Pour the blackberry-lemon mixture into each glass, filling about halfway.
Top off each glass with chilled sparkling water.
Garnish each mocktail with a sprig of fresh mint and a lemon slice.
Notes
Adjust the amount of simple syrup to your desired sweetness. For a more intense blackberry flavor, muddle a few extra berries directly in the glass before adding the liquid.