Using a sharp paring knife, peel the oranges, removing all of the bitter white pith. Cut between the membranes to release the orange segments into a medium bowl.
Coarsely grind the ancho in a spice grinder or finely chop with a knife. Transfer to a bowl and add the lime juice, oil, mint, garlic and honey. Gently stir the mixture into the oranges. Let the relish stand at room temperature for 45 minutes. Season with salt and pepper before serving.