What is the ruling of Islamic law regarding dealing with a relative who has severed kinship ties and caused harm, and is it obligatory to strive to communicate with him despite his wrongdoing, out of fear of Allah's wrath?

If relatives cut off someone who wishes to connect with them, the sin is on the one who severs ties, not on the one who tries to maintain them. It is preferable to connect with those who cut you off, to give to those who deprive you, and to forgive those who wrong you, for in this there is virtue, honor, and glory in this world and the Hereafter. Furthermore, repelling evil with good may lead to love and affection. One should also frequently supplicate for the facilitation of reconciliation and the mending of hearts.