Stir together first 7 ingredients in a large bowl; cover and chill.
Stir together soy sauce and next 3 ingredients in a shallow dish. Add mahi mahi; cover and chill 30 minutes.
Thread fish on 8 (12-inch) skewers. Grill, covered with lid, over medium-high heat (350° to 400°) 5 minutes on each side or until done. Serve with salsa mixture.