The Phnom Penh Post said a piece of unexploded ordnance went off Tuesday as the group attempted to dismantle it.
Cambodian Mine Action Centre Director-General Heng Ratana said two of the men were seriously wounded, and one was critically injured.
Three men had damage to their arms and faces, Ratana said, and all four men were transported to hospitals.
Doctors said one of the victims was being operated on for internal bleeding and damage to an artery in his leg.
The men, who came highly qualified for the job, had started their first day of a month-long teaching course when the accident occurred, The Phnom Penh Post reported.
The names of the Americans are not being released.
The Post said exploding ordnance killed 43 people in Cambodia both 2011 and 2012.