"We removed a part of his cranium to decompress his brain, which was showing significant signs of inflammation and bleeding", the hospital's director Dr Leonardo Gil told the Noticias Argentinas news agency.
Cordi remained in intensive care on Sunday evening.
He is accused of killing Coppa, his ex girlfriend, on Tuesday, when the pair met at Bariloche's iconic Cathedral.
Authorities believe Cordi was obsessed with his alleged victim, who had ended their relationship four months ago.
The Coppa family thanked "the San Carlos de Bariloche community for the moral and spiritual support we have received since this sad incident which we are dealing with, having lost our daughter and the mother of our grandchildren Valeria".