Witnesses said the mahout – the elephant’s handler –climbed down to take photos of the tourists when it hit him with its trunk and stabbed him in his body with a tusk.
The elephant is then said to have gone on the rampage, throwing Mr Crowe and his daughter off its back.
It then trampled Mr Crowe before stabbing him in the chest with a tusk, killing him instantly.
His teenage daughter, named Eilidh Hughes, escaped with minor injuries in the fall as the elephant ran off into the forest.
Witnesses said the elephant –known as Golf – had appeared upset just before the attack.
It had refused to follow the instructions of the mahout, who is believed to have hit it several times with a hook.
Mr Crowe was visiting the well-known holiday island with his partner Catherine Hughes, 42, their daughter Eilidh and her brother Mark.
The family are originally from the Isle of Islay but are believed to have moved to the Scottish mainland around two years ago.
Ms Hughes was last night at the Bangkok Hospital on Ko Samui, where her daughter is still recovering from her injuries.
She said: “My head’s all over the place. We were all here on holiday.
“My son and I didn’t go on the elephants. I’ve been given no information as to what happened or how it happened.
“Eilidh is OK but I don’t know exactly what happened.”
Asked about Thai news stories suggesting Mr Crowe may have been teasing the elephant with a banana when it bolted – which his daughter has denied on social media – she said: “I’ve seen some report on a local newspaper but I don’t know if it’s true or not true.
“All I know is what I’ve been told from Eilidh.
“It’s just myself, my son and Eilidh here. I’ve not been in touch with the British Embassy yet. I don’t know whether I’m coming or going. Right now I need Eilidh to rest.”
Writing from her hospital bed, the teenager hit out at the reports on a local news site.
She said: “He was not teasing the elephant as I was his 16-year-old daughter who is lying in hospital and I was on it. I know everything that happened. This is a serious situation.”