Peel one orange, discarding the peel. Leave the other orange unpeeled. Cut both oranges into wedges.
Place the oranges and raisins in a food processor. Pulse until roughly chopped. Add the cranberries and pulse until finely chopped but not pureed.
Transfer the relish to a serving bowl. Stir in the liqueur. Cover and refrigerate for at least 30 minutes and up to 24 hours.