In a blender, combine the fresh raspberries, peach slices, fresh lemon juice, and granulated sugar. Blend until smooth.
Pour the blended mixture into a pitcher. Add the cold water and stir well to combine. Taste and adjust sugar if needed.
Chill the lemonade in the refrigerator for at least 30 minutes to allow the flavors to meld. You can also strain the mixture through a fine-mesh sieve if you prefer a smoother texture, discarding the solids.
Serve the raspberry peach lemonade over ice. Garnish with fresh mint leaves and additional raspberry and peach slices if desired.
Notes
For a sparkling version, substitute some or all of the cold water with club soda or sparkling water just before serving.