1. In a blender or food processor, combine 1 cup raspberries and powdered sugar. Cover and blend or process until smooth, stopping to scrape down sides as needed. Reserve.
2. Cut both ends off the watermelon, leaving a thick center disk that is about 3-inches thick. Reserve the two end pieces. Trim the rind away from the 3-inch-thick disk. Transfer to a large serving platter. Refrigerate.
3. Use a melon baller to cut watermelon balls from the two reserved end-pieces of watermelon, enough to make 2 cups.
4. in a medium bowl, combine watermelon balls, strawberries, and remaining 1/2 cup raspberries. The recipe may be made up to this point, up to 6 hours ahead. Wrap everything with plastic wrap and refrigerate.
5. To serve, remove raspberry sauce, thick watermelon disk on the platter, and the mixed fruit from the refrigerator. Pre-slice the watermelon disk into 8 wedges, but keep together to form the base of the cake. Place 8 small scoops of ice cream onto the watermelon cake. Top with reserved berries and watermelon balls. Drizzle with raspberry sauce and garnish with mint leaves. Serve immediately.