What is the ruling on saying "I have disbelieved" when debating with a relative, and does that necessitate an expiation?

This statement is clear disbelief (kufr) and apostasy (riddah) that nullifies one's deeds if its utterer dies upon it. Intention is not considered in this matter; rather, apostasy is determined simply by the outward manifestation of the words of disbelief.

Slapping the face is one of the major sins and is an act of Jahiliyyah (the pre-Islamic era of ignorance).

There is no expiation for that act except repentance, regret, and the firm resolve not to return to it, along with uttering the two testimonies of faith (Shahadatayn).