Drain oranges; let stand on several layers of paper towels to absorb excess moisture. Snip orange slices in half using kitchen shears.
Combine pineapple and remaining 7 ingredients in a medium bowl, mixing well. Add oranges, stirring gently to combine. Spoon mixture into wide-mouth jars; seal and refrigerate. Serve as an appetizer with tortilla chips or as an accompaniment to chicken, fish, or pork.