Slice top and bottom off 1 orange and set on a flat work surface. Cut downwards from the top, following the curve of the fruit, to remove all of the skin and pith. Hold the orange over a bowl to catch juice; cut both sides of each segment away from the connective membrane and transfer to a separate bowl. Repeat with remaining oranges, grapefruit, and tangerine.
Gently toss oranges, grapefruit, tangerine, fennel, and onion together. Add mint, vinegar, and salt; toss gently.