To prepare tuna, combine the first 6 ingredients in a large zip-top plastic bag. Add tuna to bag; seal. Marinate in refrigerator 30 minutes, turning once. Remove tuna from bag; discard marinade. Place tuna on grill rack coated with cooking spray; grill 2 minutes on each side or until desired degree of doneness.
To prepare salad, place onion slices on grill rack coated with cooking spray; grill 5 minutes on each side or until tender. Cool and chop.
Combine vinegar and next 5 ingredients (through garlic) in a large bowl, stirring with a whisk until blended. Add onion, cucumber, parsley, capers, and beans to vinegar mixture; toss to coat. Arrange 1 1/2 cups salad greens on each of 4 plates. Top each serving with about 1/2 cup onion mixture and 1 tuna steak.