Timothy Maes, 22, was driving the green Ford pickup truck when he and his passenger, 35-year-old Jared Jacquez, drove off the cliff in the area of NM 173 and NM 511, Sheriff's spokeswoman Beth Utley said.
Jacquez, who was airlifted to San Juan Regional Medical Center following the crash, remained in critical condition Friday, a hospital spokeswoman said.
Maes, who is listed in serious condition at the hospital, told sheriff's deputies that he was driving Jacquez to medics in order to obtain help for him at the time, Sheriff's spokeswoman Beth Utley said. It remains unclear what was wrong.
Maes said he looked down for a brief moment and then crashed.
Jacquez was ejected from the truck and pinned under the right front tires, Utley said.
It took rescue personnel several minutes to reach the vehicle and free Jacquez from underneath it.
Maes was brought up to the roadway to an awaiting ambulance.
Witnesses on scene reported they "heard the truck accelerate and then the sound of crunching metal as the truck hit rocks and trees and came to rest at the bottom of the canyon."
Fishermen in the area rushed to the occupants by canoe to assist, Utley said.
Because of the steep cliff and heavy brush, rescue efforts were severely hampered.
Neither man was wearing a seat belt. Sheriff's deputies are reconstructing the crash and
Crews shut down NM 511 on Friday to recover the vehicle from the bottom of the cliff. It remained closed for about an hour.