Peel the Cara Cara orange, grapefruit, blood orange, and mandarins. Separate the segments, cut them into bite-sized pieces, and place them in a large bowl.
To prepare the cocktail citrus and ugli fruit, use a sharp knife to slice off the top and bottom. Stand the fruit on a cutting board and carefully slice away the peel and white pith, following the curve of the fruit.
Working over the bowl to catch any juices, use a paring knife to carefully cut between the membranes to release the fruit segments directly into the bowl.
Halve the washed kumquats lengthwise, remove any seeds, and thinly slice them.
Add the sliced kumquats to the bowl.
Add the finely chopped fresh mint to the bowl and gently toss everything to combine.
For the best flavor, cover and refrigerate for at least 15 minutes before serving to allow the flavors to meld.