Process first 3 ingredients in a food processor until smooth, stopping once to scrape down sides. Transfer to a bowl. Cover and chill 2 hours.
Cut pineapple in half lengthwise. Cut each half into 4 wedges.
Grill, covered with grill lid, over high heat (400° to 500°) about 5 minutes on each side, or until lightly browned.
Pour honeydew mixture into 8 chilled bowls; sprinkle with chopped mint. Arrange pineapple over honeydew mixture. Top each serving with raspberries and a mint sprig. Serve immediately.
*For testing purposes, we used Midori.