If using, prepare the bowl of the ice cream maker according to manufacturer's directions.
Place the mango chunks in the food processor and puree until smooth. You should have about 3 cups of puree. Place the 3 cups of puree in a mixing bowl and stir in the simple syrup, lime juice, and chili powder. Pour the mixture into a shallow dish and place in the freezer. Freeze for at least 3 hours and up to overnight.
If using an ice cream maker, pour into maker and freeze according to manufacturers directions. Transfer the sorbet to a freezable container and freeze until firm, about 1 to 2 hours.
Serve cold, sprinkled with a little coarse salt and more chili powder, if desired.
In a small saucepan, dissolve the sugar in the water and bring to a boil. Boil 2 to 3 minutes, then remove from the heat and allow to cool completely.