Scoop the Mango (3) and Fresh Pineapple Chunks (2 cup) into a blender. Add the Corn Syrup (1/2 cup) and Lime Juice (1/4 cup) and blend until smooth, about 30 seconds.
Pour the mixture through a strainer set over a bowl and use the back of a spoon to press the liquid through the strainer. Discard any solids.
Cover the fruit puree with plastic wrap and refrigerate until very cold, several hours or overnight.
Follow the directions of your ice cream maker and churn or freeze the sorbet until it has the consistency of soft serve - about 15 or 20 minutes. Transfer to a container and freeze for two hours until set.