Place sugar on a small plate and run a lime wedge around the rim of your cocktail glass. Place glass upside-down on plate to coat rim in sugar.
Put blackberries and diced jalapeño in a shaker and muddle as much as possible (extract as much juice as possible from blackberries and break down jalapeños)
Add vodka, simple syrup, and lime juice to the shaker along with crushed ice and shake well.
Pour cocktail into prepared glass (do not strain) and top off with a little bit of soda water. Garnish with blackberries, sliced jalapeño, and mint if desired.