I think there is a slight difference in meaning. “Cut you off” means to stop someone talking - it can mean interrupt sometimes (depends on context) but it can also imply stopping them completely. Interrupt implies you want them to carry on talking after you have interrupted to say something. I’d go with “sorry to interrupt” if you are not sure which one to use. “Cut you off” sometimes implies that you don’t agree with what someone is saying so you want to stop them from talking - it isn’t always impolite but in certain situations it could sound a bit strong which is why I say this. For example: a journalist interviewing someone who is not answering a question properly on tv - the person is talking nonsense so the journalist may say “ok, I’m going to cut you off there and ask a different question as this is going nowhere.” They would be telling the person to shut up in a polite way. However... you can say “sorry I think I cut you off by mistake” when talking on the phone. You would say this as an apology if you were talking to someone on the phone and the connection was lost or you accidentally hung up the phone in the middle of a conversation. You would call the person back and say this.

'Cut you off' suggests that you are making the person stop, not simply interupting. It is quite an aggressive action and probably wouldn't be part of an apology. A good verb for interupting would be 'sorry to butt in'.