A woman is fighting for her life after being caught in the crossfire when West Australian police shot dead a knife-wielding man who was screaming for "the head of police" and threatening to kill her.

The dramatic scenes, described as "shocking" and "terrifying" by witnesses, unfolded about 8am yesterday a Carlisle deli on the corner of Oats and Harris Sts.

The 37-year-old woman was working in the deli when the man burst in, grabbed a knife from behind the counter and dragged her outside.

Terrified customers and nearby residents watched on in horror as the 38-year-old man held the knife to the woman's throat and threatened to kill her.

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Police Commissioner Karl O'Callaghan said "a number of officers fired their weapons" after attempts to negotiate with the man failed.

The man was shot multiple times and died at the scene.

The woman also suffered a gunshot wound to the leg, and stab wounds. Police administered first aid until the ambulance arrived at the scene.

She is in a serious but stable condition in Royal Perth Hospital.

Witness Mike Shumack, 28, said: "I heard a lot of yelling and then saw there was a guy dragging this girl around. When some more policemen showed up, he seemed to get a little more aggravated.

I heard shots firing. He took a while to go down. He got shot quite a few times, eight to ten times."

Nearby resident Masery Kamara, 26, said police were telling him to "let her go, let her go".

"He took the knife to the lady's neck. The police had no choice, they had to shoot him."

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Mr O'Callaghan said the 38-year-old man who was shot dead was not known to the woman.

"The officers there were under a lot of pressure, obviously it's a complex situation, they have to make a decision in rapid circumstances," O'Callaghan said.

"It seems to me the police had to make a split-second decision.

"They can use their firearms when someone's life is in imminent danger.

"It's my belief they felt that was the case and they took action as they've been trained to take."

The Major Crime Squad is investigating the circumstances surrounding the fatal shooting, while the Internal Affairs Unit will examine the conduct of the officers involved.