Is it considered a severing of family ties if a woman reports her brother to security, given that he abuses her, seeks to expel her from the family home—which belongs to their father—constantly insults and curses, disrespects all of his siblings, and caused their mother’s illness and death?

Your brother has no right to expel you from the house as long as he does not own it. There is no blame upon you for informing the authorities about his transgressions. However, you must maintain ties with him in a way that does not harm you, even if he severs ties and is abusive, as the Prophet, peace and blessings be upon him, said: "If you are as you say, then you are feeding them hot ashes, and you will continue to have a supporter from Allah against them as long as you persist in that." However, if maintaining ties with him causes you harm, or if your severing ties with him deters him from sins and gives hope for his reform, then that is permissible.