You cut family off, by comming to terms with not having them in your life, yourself. You stop looking for advice from others around you, you stop looking outside yourself to validate your choice.
It means you cant ask your mother for advice, because frankly her advice is toxic. She is exhibiting a mentality where his decissions and actions, and the consequences thereoff, are somehow intertwined with you, and something you are partly responsible for. Like you are a damn to hold back the nasty.
Stop asking for permission.
Stop talking about the person with others who still maintain contact. Ask those people to respect your choice and impress upon them in no uncertain terms that is not up for debate. Leave the room, end the conversation, put the phone down, if they wont respect your decission to cut the person out of your life.
Usually going no contact with someone in your family, like a parent isnt that hard, unless you are still seeking permission of confirmation from others that what you have done is ok. When they sense a weakness or wavering, all their opinions, based on all their NOTLIKEYOURS experiences with said person, open a floodgate of viewpoints and critisisms that are draining to deal with if you engage.
Noone can tell you how your relationship with your father has affected you, what it keeps doing to you. Even your own mother seems to be unable to appreciate it really, putting his needs above your own. So you are experiencing that you must be ultimately alone about the decission. And why.
Lean on your significant other, be they husband or friend. - trust your world will be better not worse without his presence. Take the guilt and leave outside your home where it belongs.
You can still wish death on your father for making you go through this kind of soulsearching and for killing all the fuzzy ideas and longings we have about shitty parents. - But dont feel guilty.
I went NC with my own father over 15 yrs ago. I barely think about him anymore. The first year I recieved angry letters. I threw them out - but with each one, I imagined him on his deathbed as I tore the letter in pieces. I promised myself if that ceremony was ever hard, I'd rething the decission. But its not hard. Because I dont care if he lives or dies, so long as he does it a long way away from my life.
If thats how you feel, you can go no contact and be just fine. - Just dont make it a commitee decission. Its on you!