A parricide is a person who murders is father, mother, or other close relative. There are certain specific words to describe a person who murders a particular relative. A patricide is a person who murders his father. A matricide is a person who murders his mother. A fratricide is a person who murders his brother. A sororicide is a person who murders his sister. An uxoricide is a man who murders his wife. A filicide is a person who murders his or her child. A mariticide is a woman who kills her husband. The same words are what we call the person who commits the crime, and what we call the crime itself. Example: A person who murders his father commits patricide. Note: All of these words are rarely used. But they do exist, and you may hear or read them from time to time.

While both are gramatically correct neither is in common usage. There isn't a common phrase for this scenario. In these cases most people would interpret 'relative' as an adjective, not as a noun. Unfortuately it doesn't then make sense.

The only way to say it is to make a phrase out of it: "murderer'killer of his/her relatives"