Add 3/4 cup pineapple juice, orange juice and sugars to a medium saucepan. Cook over medium high heat, stirring constantly until sugar dissolves, 1-2 minutes.
Stir in cranberries and bring to a boil. Reduce to a simmer over medium low heat until cranberries burst and sauce reduces, about 10-12 minutes. Sauce will thicken more upon standing.
Mash berries to desired consistency (optional) then stir in all of the crushed pineapple, cinnamon and cloves. Add a dash of orange juice for tangier, sugar for sweeter if desired. Serve chilled or room temperature.
Notes
Prep Ahead
This Cranberry Sauce can be made up to two days ahead of time and stored in an airtight container in the refrigerator (tastes even better made ahead!) or frozen for up to two months.