To prepare shrimp, combine first 3 ingredients in a large zip-top plastic bag. Add shrimp to bag; seal. Marinate in refrigerator for 2 hours, turning bag occasionally.
Prepare grill to medium-high heat.
Remove shrimp from bag. Sprinkle shrimp with 1/4 teaspoon salt. Place shrimp on grill rack coated with cooking spray; grill 3 minutes on each side or until shrimp are done. Drizzle 2 tablespoons juice over shrimp; keep warm.
To prepare chutney, combine onion and remaining ingredients except the cilantro sprigs in a food processor; process until smooth. Serve with shrimp. Garnish with cilantro sprigs, if desired.