What is the ruling of Islamic law concerning severing ties with a brother who commits grave sins, mistreats his parents, and causes harm?

The Shari'ah has commanded the maintenance of kinship ties (silat al-rahim) and prohibited their severance. It has not forbidden maintaining ties with a wicked relative or a polytheist. Shunning a disobedient relative depends on what serves the greater good. If boycotting him benefits in bringing him back to the right path, then that is preferable. However, if the more appropriate course of action for him is to maintain ties while continuously offering advice, then that is preferable. It is not obligatory to maintain ties with a brother if it harms one's religion or worldly affairs. The Shari'ah has not specified a particular method for maintaining kinship ties; it can be achieved through visiting, calling, greeting, and anything that custom considers to be a form of connection. Among the greatest forms of connection is to forbid him from evil, enjoin him to good, and assist him in steadfastness.