Is reducing contact with relatives who deliberately hurt and mock one's wife, and limiting interaction to merely exchanging greetings, considered severing ties of kinship?

Kinship ties are among the greatest acts of devotion and the most obligatory duties. A Muslim must maintain ties with their kin, endure their harm, and advise them kindly. If one perceives that a legitimate (Shari'i) interest necessitates avoiding close association with relatives, there is no blame in that, and they are not considered a severer of ties. They must maintain ties with them through whatever means possible that do not cause them harm.

If their harm is related only to the wife, then severing ties is not permissible, as the wife is not among those considered kin (dhawi al-rahm). Kinship ties are not all of equal degree; there are ties that must be maintained and others that do not have this obligation.