A sister’s brother doesn’t pray and doesn’t follow the teachings of Islam. He denies some ahadith and he mocks some parts of Islam because of his ignorance. He was not raised or commanded to practise Islam by his parents. He grew up to be very angry and always fighting, being very rude to his family. His sister doesn’t speak to him because she is tired of fighting so she avoids him and they haven’t gotten along for years. He is also very violent so she fears for her safety if she makes him angry. For now her life is peaceful although they live together because they don’t speak to each other. In this case is it permissible to cut off ties with him? She still makes duaa for him.
A brother who does not pray and mocks anything of the religion is a reason to cut ties of kinship. Yet, as you said, he is ignorant. My advice to you is to first supplicate to Allah for him then try to show him some attention and try to touch his heart with the intention of calling him to the truth. You can buy him a present or send him nice messages. If his heart is opened to you then you can start talking to him about Allah and the Prophet, peace be upon him, and show him that you have mercy for him. We should not give up hope. We need to keep trying to call our families to Islam.