Cut-up frozen fruit is the trick for lightning-quick sorbet. To make ahead, freeze in an airtight container and defrost at 30-second intervals in the microwave until soft enough to scoop (about 1 1/2 minutes total). For a pretty garnish, top with paper-thin mango slices and lime rind strips.
Combine mango and sugar in a large bowl; toss to mix. Let stand 10 minutes.
Place half of mango, half of banana, and half of lime juice in a food processor; process 3 minutes or until the mango is smooth. Transfer mixture to a bowl, and place in the freezer. Repeat procedure with remaining mango, banana, and juice; combine with reserved mango mixture, tequila, and salt, stirring to mix. Spoon into bowls and serve immediately, or freeze until ready to serve.