The police have shot and killed a man who allegedly cut a woman's throat with a knife and attacked a policeman in Bendon district, St Catherine, on Sunday.

The police reportedly responded to a call about a domestic dispute about 11:30 a.m. and on their arrival observed the woman with a wound to her throat.

Her partner, who was armed with a knife, was also spotted on the veranda.

He was ordered to drop the knife, but he allegedly attacked a policeman who took evasive action and fired shots hitting the man.

The injured woman and man were taken to hospital by the police.

The man succumbed to his injuries while the woman was admitted.

The Independent Commission of Investigations has launched a probe into the matter.