Combine the blackberries, 2/3 cup water, the tequila, sugar, orange liqueur and lime zest and juice in a blender. Blend until smooth and the sugar dissolves.
Strain the mixture through a fine-mesh sieve into a large bowl or liquid measuring cup, pressing it through with a rubber spatula. Churn in an ice cream maker according to the manufacturer?s instructions until thick and slushy.
Pour into glasses and top each with 1/2 to 1 teaspoon mezcal. Garnish with blackberries.
Photograph by Levi Brown