It might mean no longer supporting someone. A parent might decide to stop paying for a child's education if they were no doing well, in which case they would cut the child off. In driving, if a person pulls their car in ahead of you and blocks you from getting in someplace, they have cut you off. You can cut somebody off by interrupting what they are saying. As Jakir_UK says, you can hang up on them on the telephone.

I think it means when you take someone out of something, such as maybe a plan or it could be betrayal or leaving them isolated, or it could mean when someone gets cut off deliberately during a phone call? Hope that helps. :)