Christ's new commandment in John 13:34 would actually be a replacement of all those other commandments, including the big ten. The ten commandments were part of the old covenant God made with the nation of Israel through Moses on Mt. Sinai and Jesus fulfilled the law upon his death and resurrection.
Does that mean we can then go around murdering each other? No, because murdering each other would not be loving one another as Christ loves us.
Does that mean we can go and commit adultery? No, because committing adultery is not loving to the person who is betrayed or even to the other person in the affair.
See where this is going? New covenant Christians are not under the yoke of law, but under grace, and when we show Christ's love to one another, we are in full alignment with the Holy Spirit.