No, a Catholic wedding ceremony cannot take place on the beach in Mykonos. Catholic weddings in Greece must be held inside a Catholic church and follow the guidelines set by the Catholic Archdiocese.
In Mykonos, the Catholic Church of Panagia Rodario in Mykonos Town is the only approved location for a Catholic wedding. If you dream of a beach ceremony, you may consider having a symbolic ceremony on the beach after your official Catholic wedding in the church.