Spoon 3 Tbsp. juice from mangoes into a shallow dish; pour mangoes and remaining juice into a blender.
Dip rims of glasses into 3 Tbsp. mango juice; dip in sugar crystals to coat.
Add limeade concentrate, tequila, and orange liqueur to blender; process until smooth, stopping to scrape down sides. Reserve half of mixture in a small pitcher.
Add ice to remaining mango mixture in blender to 5-cup level; process until slushy, stopping to scrape down sides. Pour into prepared glasses. Repeat procedure with reserved mango mixture and additional ice. Serve immediately.
Note: We tested with Triple Sec for orange liqueur.