Justine Damond (40) formerly of Sydney, died in Minneapolis at about 11.30pm on Saturday after two officers responded to a report of a possible assault.
Her stepson Zach Damond says Ms Damond called police after hearing a sound in the alley behind her house in the suburb of Fulton.
"My mum was shot for reasons I don't know," Mr Damond (22) said in a video posted on Facebook.
"America sucks, these cops need to be trained differently and I need to move out of here," an emotional Mr Damond said.
He added that his stepmother was a "very passionate woman" and that police had taken his "best friend's" life.
Ms Damond, also known as Justine Ruszczyk, was a vet who worked as a spiritual healer and meditation teacher.
She ran her meditation workshops at the Lake Harriet Spiritual Community, which paid tribute in a Facebook post.
"We are so sad to report the tragic shooting of Justine Damond," the community's post said.
"Justine was one of the most loving people you would ever meet. We can't even imagine LHSC without her."
Ms Damond is believed to have been living in the US for at least the past three years.
It has been reported she was due to marry her fiance Don Damond (50) next month.
Minneapolis mayor Betsy Hodges wants to know why the officers' body cameras were switched off.
"I am heartsick and deeply disturbed by what happened," she posted on Facebook.
"I have been working on behalf of all of you all night and all day and I will continue to do so.
The Minnesota Bureau of Criminal Apprehension said two Minneapolis police officers responded to a 911 call of a possible assault just north of the 5100 block of Washburn Avenue South.
"At one point an officer fired their weapon, fatally striking a woman," it said in a statement.
"The officers' body cameras were not turned on at the time and the squad camera did not capture the incident.
"Investigators are attempting to determine whether any video of the incident exists."
Ms Damond's personal website says she trained as a veterinarian and practised yoga and meditation for 17 years.
The Department of Foreign Affairs and Trade says it's providing consular support to the family of an Australian woman killed in the US.