For sauce, in a blender or food processor combine salsa, coconut milk, green onion, lime peel and juice, cilantro, mint, curry paste, ginger, soy sauce, and garlic. Cover and blend or process until nearly smooth. Remove 1/3 cup of the mixture for sauce; cover and chill until serving time. (Or use it all for sauce/dressing!).
Place chicken in a large resealable plastic bag set in a shallow dish. Pour remaining marinade over chicken; seal bag. Marinate in refrigerator for 1 to 2 hours, turning bag occasionally. Drain chicken, reserving marinade.
For a charcoal grill, grill chicken on rack of an uncovered grill directly over medium coals for 12 to 15 minutes or until chicken is no longer pink (170 degrees F), turning once and brushing with reserved marinade halfway through grilling. (For a gas grill, preheat grill. Reduce heat to medium. Cover and grill as above.) Serve chicken with mango and cucumber. Drizzle with reserved 1/3 cup marinade mixture. If desired, garnish with mint.