Zest both blood oranges using a microplane zester. Then peel then oranges and discard the peels and pith.
In a high-powered blender, combine the blood orange zest, orange segments, strawberries, banana, yogurt, milk, and sweetener, if using.
Blend on high until very smooth. Because of the membranes surrounding the blood orange segments, you’ll want to blend longer than you normally do to make sure they are really well mixed in.