It doesn't mean to cut off with your relatives (especially with parents). You cannot cut off with your parents and other relatives until they compel you to obey or accept their religion. Allah clearly mentioned in [Luqman 31:15]:
"But if they (both) strive with you to make you join in worship with Me others that of which you have no knowledge, then obey them not; but behave with them in the world kindly, and follow the path of him who turns to Me in repentance and in obedience."
Read the following statement from IslamQA:
The scholars of the Standing Committee for Issuing Fatwas were asked:
I have family who is mushrikeen (polytheists) except one sister who is a Muslim. Is it permissible for me to live and eat and drink with them, and if that is permissible so long as it is not at the expense of my religious commitment, then it is permissible for me to tell them frankly that they are kaafirs who are outside of the religion of Allaah? I have called them to Islam but they are hesitant, and they do not belong to this group or that, although they are closer to shirk, and I cannot find anywhere to live except with them.
What you must do is continue to advise them, remind them, keep good company with them, and speak gently to them. If you are wealthy, then spend on them, in the hope that Allaah may open their hearts and show them the light.
So finally, this doesn't mean to cut off with your relatives.