In a blender, combine the fresh raspberries and diced peaches. Blend until smooth.
Strain the blended mixture through a fine mesh sieve into a bowl to remove the seeds and pulp, using a spatula to press the mixture through.
In a large pitcher, mix the strained raspberry-peach puree with freshly squeezed lemon juice and granulated sugar. Stir until the sugar is fully dissolved.
Add the cold water to the pitcher and stir well to combine. Adjust sweetness by adding more sugar if desired.
Refrigerate the lemonade for at least 30 minutes to chill and allow the flavors to meld.
Serve over ice cubes in glasses and garnish with fresh mint leaves.
Notes
Adjust the sugar to taste based on your preference for sweetness.