Combine granulated sugar and filtered water in a small saucepan over medium heat, stirring until the sugar is fully dissolved.

Remove the simple syrup from heat and allow it to cool completely to room temperature.

In a large punch bowl or pitcher, combine the fresh lemon juice and the cooled simple syrup base.

Slowly pour in the chilled sparkling mineral water, stirring gently to maintain carbonation levels.

Add the lemon slices and mint leaves to the bowl for flavor infusion and visual presentation.

Serve immediately in glasses filled with ice cubes.