The accident occurred Sunday on Interstate 84 near Pendleton, The (Portland) Oregonian reported Monday.
About half of the injured were hospitalized, officials said.
Rescuers used high-angle techniques and an all-terrain vehicle to lift injured passengers and bodies up Cabbage Hill along Deadman Pass, The Oregonian said.
"'Organized chaos' is how I would describe it," Pendleton Fire Chief Gary Woodson said.
The bus driver survived with severe injuries and had been unable to provide information about the crash, police said.
Umatilla County Emergency Manager Jack Remillard said the bus is owned by MiJoo Tour & Travel in Vancouver, British Columbia.