Graves have been destroyed, knocked over and vandalised at the Church of Ireland Killeshin Church, Graiguecullen.
Anthony Heaney of It's All About Carlow came upon the devastation and said earlier this week and said: "Over 20 graves at Church of Ireland cemetery have yet again been vandalised for the third time.
"At the moment there is no known reason as to why the shocking attacks were carried out."
Cllr Walter Lacey said: "It's not the first time it's happened, it's appalling that it should happen. Parents of these people must accept responsibility. Where are the parents of the people that have been carrying out these acts?
"To carry out vandalism on those that are past and rested, it's such a sensitive issue for families who care for their loved ones in these cemeteries and graves."
Earlier this week a councillor hit out over an act of vandalism at the Croppies Grave monument in Carlow where flower beds were destroyed.