For example, he just "disowned his friend" or "broke up with his friend" or "broke off the friendship with his friend". Which are correct? Is there any difference between correct ones"?
"Broke up with" is normally used to describe ending a romantic relationship. For example, "He broke up with his girlfriend". The two people might or might not remain on friendly terms. Note this is only used for a dating relationship, not marriage. If you end a marriage, then it's "They got divorced" or "They separated".
"Broke off the friendship" is used to describe ending a non-romantic relationship. This always means that the two people had some sort of argument or sharp disagreement. Like, "When Al learned that Bob had lied about him, he broke off the friendship." You would not use this phrase to describe two people who just "drift apart". Like if one person moves to another city and so they don't see each other very often, at some point you might say that they aren't really friends any more, but no one "broke it off", it just happened.
To "disown" someone is to renounce responsibility for them. I think it's most often used to describe a parent completely cutting ties to a child. Like, "After Sally was arrested for the fourth time, her father disowned her." Normally this would only be used to talk about a child who has reached adulthood, or at least late teens. People do sometimes talk about a child disowning a parent or someone disowning a brother or sister. It is considered a very severing of the relationship, the "moral equivalent" of divorce. It may include legal steps, like removing the person from your will.
Occasionally someone will say that he disowned a friend, but I think this is pretty rare, as to "disown" something you had to first "own" it, and we don't normally think of friendship as being that tight. It's normally only used for family relationships.