Place cut mango, orange, lemon, and lime in a large pitcher. Pour in the lemonade and the Rioja and stir well.
Taste test the sangria. It should be sweet and a bit tart; it will get sweeter as the fruit juice blends into the drink. If you'd like the sangria to be sweeter, add 1 tablespoon of granulated sugar at a time (up to a maximum of 3) until desired sweetness is reached.
Let sangria sit in the refrigerator for at least 6 hours or ideally overnight.
Serve mango sangria with additional orange slices, if desired.