The defrockings come one day after the Pope accepted the resignation of a United States cardinal who was accused of covering up a sex abuse scandal in Pennsylvania.
Defrocking is considered the harshest penalty for priests within the Church and means the offender is forbidden from exercising any clerical duties at all.
Ireland has had a tumultuous relationship with the Catholic church in recent years particularly due to revelations of sexual abuse within many dioceses in the country, the existence of the Magdalene laundries and the churches hardline stance against abortion.
"The civil investigation is still ongoing because he's never responded to a court subpoena to give testimony", Vatican expert Ms San Martin said. It is believed he is in poor health.
The allegations of abuse against Cox date back to the 1970s.
In a statement, the Schoenstatt Fathers reaffirmed its "willingness to collaborate" with anything that the judicial authorities required.
The expulsions come a few weeks after the pope defrocked Chilean priest Fernando Karadima, who was found guilty by the church in 2011 of sexually abusing minors.
But if pope Francis had accepted a number of resignations of bishops from chile, this is the first time that it makes both to the lay state.
Cox, who is believed to have returned to Germany after a period in Chile, could not be reached for comment.
"Now it's up to the Chilean justice to do something!" Un buen día para los sobrevivientes de estos monstruos.