A simplified, streamlined, Scriptural, balanced view of Shunning and Disfellowshipping:
Jesus said to treat people who unrepentantly harm you and don't apologize, as people of the nations or as tax collectors.
Jesus set the example by still being kind and friendly to tax collectors and Gentiles, even though He may not have had them as His closest friends. Jesus also made a big point of being kind and eating with prostitutes and many other sinners.
In this case, it would be the individual Christian choosing not to closely associate with people who intentionally callously harm them, which is wise. This is not a mandatory shunning enforced by the Congregation.
In Christ's parable of the Prodigal Son, He shows the attitude we should have toward those who leave the Congregation and say they don't want to have anything to do with it anymore. We should respect their choice, and be ready to welcome them wholeheartedly when, or if, they return.
Jesus' other parable of the Lost Sheep shows how we should act toward those who may have been stumbled or have doubts: We should lovingly seek them out to help them return.
The Apostle Paul said people in the Congregation who flagrantly commit sexual sins such as incest, should be excommunicated. The Congregation should not allow them any privileges or have close friendship with them, or make it look like they approve of the sins.
In addition, Paul also taught that people who openly contradicted the Congregation leaders, stirring up divisions, and causing doubts, should be given two warnings, then they should be marked by the Congregation, but they should still be viewed as brothers and sisters.
The Apostle John said that a person who contradicts the main Good News about Jesus and what He did, should be totally shunned, to the point of not saying a greeting to him or showing support for him.
I would say that none of these commands in the New Testament would support cutting off family relationships, except perhaps John's command about not speaking to those who are anti-christ.