Use a sharp knife to slice off each end of the blood oranges, then, following the curve of the fruit, remove the peel and white pith in large vertical pieces. Place a mesh strainer over a small bowl, then segment the oranges and let them fall into the strainer. With your fingers, break the segments into smaller pieces. Set aside.

In a medium bowl, fold together the avocado, red onion, jalepeno, cilantro, lime juice, and a sprinkling of salt. Add the orange segments from the strainer to the avocado mixture and fold gently to combine. Discard the juice, or reserve it for another use. Serve the salsa immediately.