Athanassios Arvanitis, 31, carried out the gruesome act on the island of Santorini following a heated argument with partner Adamantia Karkali, 25, police said.
Neighbours claimed Arvanitis also beheaded his girlfriend's dog with a butchers knife before turning the blade on his victim.
He then picked up the severed head of Ms Karkali and roamed through the streets of Vourvoulos while villagers fled inside their homes and called the police.
When police attempted to arrest Arvanitis, he pulled a knife and stabbed one officer before flinging the head of his victim into a patrol car, local officials confirmed.
The cook then stole a second patrol car sparking a high-speed police chase in which he ran over two women doctors who were riding a motorcycle.
During the chase, Arvanitis was shot five times by police as he attempted to flee before he was finally forced to stop the car.
Arvanitis, who worked at a local restaurant suffered serious injuries and was undergoing surgery at a hospital on the island, said Chrysanthos Roussos, head of the Santorini district.
One of the two doctors hit by Arvanitis suffered multiple fractures in the collision. The other was uninjured.
A female bystander was also hit by a stray bullet as police fired at the suspect. She escaped serious harm.
Angelos Roussos, the mayor of Thira, the island's main town told TV station Antenna that Ms Karkali had worked as a teacher in a local village.
Santorini is a small, circular archipelago of volcanic islands located in the southern Aegean Sea, about 200 km southeast from Greece's mainland.
Its nightlife and physical beauty have made the island a tourist hotspot for European travellers.