"It's 71 (dead). Just for Oaxaca," said Jesus Gonzalez, a spokesman for the state civil protection authority.
At least 15 people died in the neighbouring state of Chiapas, according to local authorities, while another four deaths have also been confirmed in the state of Tabasco to the north.
The 8.1-magnitude quake that struck off the coast of Chiapas on Thursday was stronger than a devastating 1985 quake that flattened swathes of Mexico City and killed thousands.
Relief efforts in the south continued through Saturday, with many of the people worst affected still wary of returning indoors to weakened buildings, fearing they could be brought down by ongoing aftershocks.
Teams of soldiers and federal police armed with shovels and sledgehammers fanned out across neighbourhoods to assist in demolition of damaged buildings.
Dump trucks choked some narrow streets as they began hauling away the many tons of rubble.
Work by residents to clear the streets and lots that held their collapsed homes was slowed by aftershocks throughout Saturday.
There were scenes of mourning in Juchitan, where a third of the city's homes collapsed or were uninhabitable, Mexican President Enrique Pena Nieto said. Part of the city hall collapsed.
On the outskirts of the city, the general hospital continued to settle into its temporary home - a school gymnasium with gurneys parked atop the basketball court.
The earthquake rendered the hospital uninhabitable, so the gym contained a mix of patients that pre-dated the quake and those who suffered injuries as a result of it.
Pope Francis, addressing an open air mass on a visit to Colombia, said he was praying "for those who have lost their lives and their families".