Is it a sin to cut ties with a relative who spoke ill of me behind my back, and must I reconcile with him?

The one who informed you about someone's backbiting has committed a sin, for his informing is tale-bearing (namima), which is one of the major sins and indicates the wickedness of its perpetrator. Therefore, he must repent. We advise you not to believe this tale-bearer and to deal with him in the way Imam al-Nawawi mentioned for someone to whom tale-bearing has been conveyed, which comprises six matters: not to believe him, to forbid him, to hate him for the sake of Allah, not to entertain evil thoughts about the person about whom the tale was carried, not to let what was narrated to him lead him to spy, and not to approve for himself what the tale-bearer forbade. Thus, you should not think ill of the backbitten person, nor should you speak to him about the matter.