Thaw tuna, if frozen. Cut into 1-1/2-inch cubes. Place in a 1-gallon sealable plastic bag. Add soy sauce, sesame oil, chopped green onion, and ginger. Seal bag; gently turn to coat tuna. Let stand 20 minutes. Drain, reserving marinade.
Thread tuna, mango, sweet pepper, and green onion pieces onto four 8-inch skewers. Place skewers on the rack of the grill directly over medium-high heat. Grill for 6 to 9 minutes or until desired doneness, turning several times and brushing with some of the reserved marinade during last 5 minutes of grilling.
Bring remaining marinade just to boiling in a small saucepan. Remove from heat; stir in honey. Brush skewers with heated marinade just before serving. Pass any remaining heated marinade. Makes 4 servings.