Place the beets, unpeeled, in a foil-lined baking dish. Cover with more foil and seal the edges of the top and bottom layers of foil to completely enclose the beets. Place them in a 400 degree oven and bake for approximately 20 minutes or until the beets are tender when pierced with a sharp paring knife.
While the beets are baking peel the oranges. First cut a thin slice from the top and bottom of the orange so that it can sit firmly on the countertop. Using a sharp paring knife cut the peel and pith off with sawing downward strokes so that the orange is completely peeled. Cut the individual sections out from the membranes. Place in a mixing bowl together with the onion and mint.
When the beets are tender hold them under running water and slip the skins off. Trim the stem end, then cut them in half and then into slices. Add the beet slices to the bowl with the oranges. Season with salt and pepper to taste than drizzle the orange olive oil over to taste. Toss to mix. Can be served immediately or allowed to marinate up to 2 days.