In a blender, combine the chopped pineapple, sliced strawberries, and 2 cups of cold water. Blend until smooth.
Strain the blended mixture through a fine mesh sieve into a large pitcher to remove the pulp, pressing down with a spoon to extract as much liquid as possible.
Add the remaining 2 cups of cold water, sugar, and lime juice to the pitcher. Stir well until the sugar is dissolved.
Taste the agua fresca and adjust the sweetness if necessary by adding more sugar.
Chill in the refrigerator for at least 30 minutes before serving.
Serve over ice and garnish with fresh mint leaves if desired.