Is it considered a severing of kinship ties if I can no longer bear to see my family after they accused my mother of performing sorcery?

You have the right to be angry with those who falsely accuse your mother and to dislike seeing them. However, it is obligatory to maintain ties of kinship with unmarriageable relatives (mahārim) such as fathers, grandfathers, brothers, sisters, paternal uncles, paternal aunts, maternal uncles, maternal aunts, and those in a similar position. This should be done through the minimum level of communication, such as returning greetings, and by showing kindness to them and being patient with their harm. This is based on the Prophet's (peace and blessings be upon him) saying: "If you are as you have said, then it is as if you are feeding them hot ashes, and you will always have a supporter from Allah against them as long as you persist in that [right]." Permissible abandonment (hajr mashrūʿ) is allowed within its specific guidelines.