A Greek man is in a critical condition after decapitating his girlfriend with a cleaver and parading her head around the tourist island of Santorini yesterday.

Athanassios Arvanitis, 31, is also accused of beheading the woman's dog before roaming around the village of Vourvoulos with his 25 year-old girlfriend's head.

"The suspect was spotted walking around, carrying the victim's head and telling the astonished villagers not to stop him" said a policeman.

"They knew he had psychological problems ... but they didn't expect he would reach this point."

When police attempted to handcuff him, the suspect knifed the officer and threw the victim's head into a patrol car. He then fled in the police car before injuring two female doctors after crashing into their motorcycle.

A third woman was struck by a ricocheting police bullet.

Arvanitis was shot five times by police during the chase and he is now undergoing surgery at an island hospital.

The victim, 25-year-old Adamantia Karkali, was a teacher at a local village.