In the bottom of a tall glass, muddle together the lime slices and fresh blueberries until mashed and juicy. Place the mint in the palm of your hand and clap about five times. This lightly bruises the leaves and releases their flavor. (See Note)
Add the rum and simple syrup and stir to combine. Fill the glass with ice and top with club soda. Garnish with additional blueberries and lime slices.
By stirring in the slightly bruised mint leaves instead of shaking vigorously in a cocktail shaker, your blueberry mojito will taste less "grassy".