Make syrup. Add the peaches, raspberries, sugar, and water to a small saucepan and bring to a boil. Reduce to a simmer and cook for 7-10 minutes, until the raspberries break down and the peaches are very soft.
Strain. Using a mesh strainer, strain out the solid fruit bits. Press with a wooden spoon to extract all the syrup. Be careful not to press too hard to avoid fruit bits in your tea. Let the syrup cool.
Brew the tea. Place the tea bags in a heat-proof pitcher. Boil 6 cups of water and pour it over the tea bags. Steep for 3 minutes, then remove and discard the tea bags. Pour 6 cups of cold water into the pitcher to cool the tea.
Add the syrup and chill. Add the peach raspberry syrup to the tea and mix thoroughly. Place the pitcher in the refrigerator to chill for at least 2 hours, or until very cold.
Serve. Serve the tea over ice with fresh lemon slices, whole raspberries, and mint leaves for garnish.