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A three-year-old girl has had her head chopped off in a savage and apparently random attack outside a Metro station in Taiwan.

Local media said police arrested a man following the attack in the capital Taipei.

According to reports, the man grabbed the girl from behind and decapitated her with a cleaver as she rode on her balance bike down the street with her mum.

The mother, who was taking the girl to see her grandfather, desperately tried to prevent the attack but could not save her daughter.

People nearby grabbed the attacker and called the police, who arrested the man when they arrived.

The girls' parents and grandfather were seen weeping over the body.

"Society is sick," the distraught grandmother told reporters.

Yang Kun-ming, head of the investigation unit of the Taipei City Police Department's Neihu Precinct, said cops were still trying to discover the man's motive.

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Hours later, an angry crowd gathered outside the police station where the man was taken.

The government-run Central News Agency said the 33-year-old had been arrested for drug crimes and treated for mental illness.

A hospital confirmed that the suspect had sought treatment there once in 2014, but added that this does not necessarily mean he has a mental illness. The man admitted to taking drugs but a test came up negative, the hospital added.

Police said the the suspect, identified only by his surname Wang, has been convicted for drug offenses and is currently unemployed.

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Politician Wang Yumin angrily declared he would push for the death sentence of the killer as soon as possible by amending the law.

If it was a random killing, it will be the third incident like it in Taiwan in four years.

Last year, an intruder snuck into a school bathroom in Taipei and slashed the throat of an 8-year-old girl.

In 2012, a man cut the throat of 10-year-old boy in a bathroom at a video game arcade in Tainan in the south of the country.

Social media users were furious about the incident.

"Animals are better than this," one person wrote, while another comment read: "Execution on the spot. A life for a life."