Home invader shot dead by cops after stabbing woman

A man who stabbed a woman and carjacked two vehicles after a reported home invasion has been fatally shot by police.

Officers were called to a property in Tuncurry on the NSW mid north coast on Friday morning following reports of a home invasion by a man armed with a chainsaw and knife.

The man, estimated to be about 41, is believed to have stabbed the 28-year-old woman, fled the house in a ute and then carjacked a four-wheel drive before police began their pursuit.

He drove the four-wheel drive through a sportsground, crashed it on the Forster Bridge, and then stole another vehicle.

The man rammed his car into the police vehicle, causing an officer to suffer minor injuries, before officers chased him to a nearby address.

The 41-year-old, still armed with a knife, entered the home and tried to carjack another vehicle.

He left a few moments later, confronted police and ran into a neighbouring property.

Offers tasered the man multiple times before he ran towards an officer, who shot him dead.

Police believe he was in a de facto relationship with the woman he stabbed and are examining the role of domestic violence.

She was airlifted to John Hunter Hospital and remains in a serious but stable condition.

"This was a very life-threatening incident," assistant commissioner David Waddell told reporters on Friday.

"Police go to work every day to protect the public.

"Unfortunately on this occasion they had to use lethal force ... but that was only after multiple attempts to stop this man using a taser and there was a direct threat to the police officer's life."

NSW Police have declared a critical incident and have launched an investigation that will be monitored by the Law Enforcement Conduct Commission.