Prepare agave syrup by diluting agave nectar with water in 1:1 ratio.
Cut out the thin wedge out of a small mango and set aside. Peel the rest of the mango and dice it into small chunks.
In a blender, combine mango, Arrogante Reposado, orange liqueur (such as Triple Sec or Cointreau), freshly squeezed juices of lemon and lime and agave syrup. Pulse several times to combine the ingredients. While continuing to blend the cocktail start adding ice chunks, several pieces at a time, until the cocktail reaches the desired consistency and thickness.
Pour the drink into a chilled cocktail glass and garnish with the reserved mango slice and a pinch of chile.