In a blender, combine grapefruit juice, orange juice, soda water and agave; blend for a few seconds to combine.

Before adding ice to blender, prepare highball glasses by muddling six blackberries in the bottom of each glass until fruit is jammy.

Add ice cubes to blender mixture, and blend until a slushy consistency forms.

Pour slushy over blackberries, and garnish with a lime slice and mint sprig.