You did not cut your Dad off, he cut you off, your mum is wrong. You asserted your independence but your father should never have given you that ultimatum, he's definitely in the wrong. Supporting someone (financially, emotionally etc) does not give that person 'power' over you, even though you dad obviously saw it that way. Supporting someone is supposed to be helping them, not controlling them.

You are amazing for standing your ground at such a young age. Your dad sounds like a bully who needed control, I think your mum is somewhat deluded if she supports your dad on this.