Combine cabbage, mangoes, carrot, celery, and green onions in a large bowl; toss until mixed.
Combine peanut butter, lime juice, water, soy sauce, cilantro, garlic, and ginger in a food processor; blend until smooth and the consistency of rich cream. Add 1 to 2 tablespoons water if dressing seems too thick.
Pour dressing over cabbage mixture; toss to distribute evenly. Sprinkle chopped peanuts on top.