Put the yuca pieces in a heavy-bottomed saucepot and cover with cold water. Season with salt. Bring to a boil and cook until tender, about 10 minutes. Drain and set aside to cool.
Meanwhile, add the vinegar, lime juice, sour orange juice, olive oil, garlic and red onions to a bowl. Season with salt and pepper. Add the cooled yuca and allow it to marinate for 30 minutes. Just before serving, stir in the parsley.