Is it permissible, to cut relations with a relative or close family friend who is a female, who despite all warnings is intent on marrying a non-Muslim?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

You should spare no efforts to prevent this woman from committing this major evil.  You may seek the help of good women or contact any Islamic Centre urging them to try their best to stop her from this repulsive act.  You should also inform her family members; probably they may stop her from getting married to a non-Muslim.

Moreover, you should not only cut all your relations with this woman as long as she is insisting on committing this sin but also it is forbidden to have any personal relation with an alien members of the opposite sex.

Allah knows best.