The storm made landfall in Mexico for a second time during the night near Tecolutla in Veracruz state as a major Category Three storm, triggering warnings of mudslides and significant floods.
The streets of Tecolutla, home to about 24,000 people, were littered with fallen trees, signs and roof panels.
Esteban Dominguez's beachside restaurant was reduced to rubble.
"It was many years' effort," he said.
"Over there was my house, but it's destroyed. I'm left with no roof or furniture," he told AFP.
In the Veracruz state capital, Xalapa, streets were turned into muddy brown rivers. Many homes in the region were left without electricity after winds that clocked 125 miles (200 kilometers) per hour.
"Unfortunately, we have seven deaths" in Xalapa and one more in the city of Poza Rica, including minors, Veracruz Governor Cuitlahuac Garcia told a news conference.
Flooding was also reported in parts of neighboring Tamaulipas state, while in Puebla in central Mexico trees were toppled and buildings suffered minor damage.
Grace weakened to a tropical storm as it churned inland, clocking maximum sustained winds of 45 miles per hour, according to the US National Hurricane Center (NHC).
At 1800 GMT, the storm was located 35 miles northwest of Mexico City, which was drenched by heavy rain, and moving west at 13 mph, forecasters said.
A man walks in a flooded street due to heavy rains caused by Hurricane Grace in Tecolutla in eastern Mexico.