Over a small bowl, supreme the blood oranges: Start by removing the top and bottom of the oranges, then place one of the flat ends of the orange on your cutting board and cut the skin off the outside while preserving the round shape. Be sure to remove all of the white pith. Pick the orange up and cut each section out of the orange in between the membranes. You will have lovely tender sections of the orange without any of the white membranes. You will be left with a "skeleton" of the orange. Squeeze the remaining juice out of the skeleton into the bowl. Repeat with the grapefruit and halve the segments.
Toss the onions and chile into the bowl with the fruit and juice and season with a pinch of salt and the olive oil. Let sit for at least 20 to 30 minutes. Stir in the mint right before serving.