Preheat the oven to 400 degrees F.
If using baby beets wrap 3 to 4 beets together in foil packets and place them on a baking pan; if using large beets, wrap them individually. Roast the beets until they're tender and a paring knife slips easily into their centers, about 20 minutes for baby beets and 30 to 40 minutes for large beets. Remove the beets from the oven and, once cool enough to handle, open the foil packages.
Meanwhile, peel and segment the oranges. Cut off the tops and bottoms of the oranges so that they sit flat on the cutting board. Using a sharp paring knife, slice off the skin from top to bottom, removing the peel and pith so that no white is left on the orange. Slice along each membrane to cut out the individual segments. Place the segments in a large bowl. Add the onion, olives, and mint.
Using a paper towel, rub the skins off of the beets. Cut the beets into quarters. Add them to the bowl with the oranges, season with salt and pepper, and then drizzle some olive oil and lime juice over the salad. Toss and serve immediately.