Place mango pieces on a baking sheet lined with plastic wrap; freeze at least 4 hours. Remove from freezer; let stand 10 minutes.
Place mango pieces in a food processor or blender; process until smooth, scraping sides of bowl occasionally. Add sugar, banana, and lime juice. With food processor on, slowly spoon yogurt through food chute; process until smooth, scraping sides of bowl once. Spoon mixture into a freezer-safe container; cover and freeze 3 hours or until firm.
Note: Let the Mango Freeze soften a little before serving.