Railway authorities say they are investigating the accident, which happened in Yilan County at about 16:50 local time (08:50 GMT) on Sunday.
A total of 366 passengers were on the train when all eight of its carriages derailed. All have been accounted for.
The incident is Taiwan's worst rail accident in 27 years. At least three children were among the dead.
"The train was going very fast. I hit a wall when the car started to flip. Around five to six people were thrown out of the carriage door," passenger Henry Tseng told Reuters news agency.
"There [was] no time to think what happened. Everyone was in a rush to get out."
The Puyuma Express 6432 service came off the tracks close to Xinma station, near the town of Su'ao about 70km (43 miles) from Taipei.
It was travelling between Taipei and the eastern county of Taitung.
"There are four carriages that were overturned at 90 degrees and the worst casualties were in those carriages," said Jason Lu, head of the Taiwan Railways Administration (TRA).
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