The pachyderm launched its attack Monday on the resort island of Ko Samui, throwing Gareth Crowe, 36, and his daughter, Eilidh Hughes, to the ground. Rambo then gored Crowe with his tusk and stomped on him.
The animal — who's also known as Golf — became enraged after its trainer, or mahout, climbed off to take a picture of the tourists.
Crowe had a prosthetic leg and was unable to run away from the elephant, officials say.
Hughes and the trainer, Zaw Win Tun, were injured in the deadly attack.
There was speculation that the elephant might have been in a state of musth, when it becomes more aggressive during its mating cycle, but authorities said that was not the case.
"We suspect that the hot weather made the elephant angry and that he was not accustomed to his mahout," Paiboon Omark, Samui district chief, told AFP.
The elephant has been chained to a tree since Monday so officials can monitor its behavior, the Bangkok Post reports. Officials say Rambo will take a 15-day break from work and then be moved to another branch of the trekking company.
Elephants are Thailand's de facto national animal and were once featured on the country's flag. Their numbers have declined in recent decades as expanding human settlements have reduced their natural habitats. Thailand now has fewer than 3,000 wild elephants and about 4,000 domesticated elephants, according to the National Parks, Wildlife and Plant Conservation Department.
The animals once were used for logging, but deforestation and a subsequent ban on most logging has led to many elephants now being used as tourist attractions.
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