Heat 2 cups mango juice, sugar, and salt in a 2-qt. saucepan over medium-high heat and cook, stirring, until sugar dissolves. Remove from heat and stir in remaining 2 cups mango juice and lime juice; let cool.
Pour into an 8″ × 8″ baking dish and place in freezer. Freeze, scraping and stirring mixture with a fork thoroughly every hour as ice crystals form to prevent it from freezing into a solid mass, until mixture is the consistency of shaved ice, about 4 hours. Spoon into chilled bowls to serve.