In a medium saucepan over high heat, combine the first 3 ingredients. Bring to a boil, reduce heat, and simmer for 3 minutes. Place peach mixture in a blender. Remove the center piece of blender lid (to allow steam to escape) and cover the top with a clean dish towel. Puree until smooth. Pour into a large bowl. Refrigerate for at least 3 hours.
Press peach mixture through a sieve over a large bowl, reserving liquid. Discard the peach solids. Stir in lemon juice.
When ready to serve, add 1/2 cup ice to the glasses, and pour peach lemonade into the glasses. Garnish with peach wedges and mint.