In a small pot add the water, sugar, and mint leaves. Bring to a boil, then cook for a couple minutes until sugar dissolves, stirring often. Remove from heat and set aside to let cool.
In a blender, add almost all the peaches (leave a handful out for garnish), the coarsely chopped cucumber and water, blend until smooth. Strain the purée to remove any large chunks.
In a pitcher, add the simple syrup (too taste), lemon juice, and peach purée. Stir to combine. Add sliced peaches, sliced cucumber and 5-6 mint leaves. Store in fridge until ready to serve. Just before serving add the sparkling water and serve over ice.
Peeling the cucumber creates a less green drink.