"F--k this guy," one of the officers can be heard saying, before the car is seen turning toward the man, who has been identified as 50-year-old Joseph Mann. "I'm going to hit him."
"Okay, go for it. Go for it," his partner can be heard responding.
The footage and audio, published on Friday by the Sacramento Bee, show Mann twice dodging the moving police cruiser, before officers stop the car, run after Mann, and fire 18 shots, 14 of which struck him.
The officers had been responding to calls of a man seen acting erratically and holding a knife and gun - police later reported recovering a knife with a four-inch blade, but no gun from the scene.
Watch the video below:
Separate dash-cam footage from another police cruiser that responded to the scene shows Mann telling officers he had no gun, and ignoring officers' commands to "get on the ground" and drop the knife.
Mann was "displaying obvious signs of mental distress" during the moments that led up to the fatal encounter in July, according to documents obtained by the Washington Post from a federal lawsuit filed by his family.
Police also said a toxicology report found methamphetamine in Mann's system.
"Inexplicably, the Officers failed to contact any properly trained mental health counselors or make any attempt to use less than lethal force and ignored the established police protocols to make attempts to de-escalate the situation," the lawsuit said.
The officers involved, Randy Lozoya and John Tennis, have been placed on "modified duty," a police spokesman told the Sacramento Bee.
"They are officers that shouldn't be in uniform," Mann's brother Robert told the newspaper. "If this is their state of mind when they go to work, this doesn't serve anyone well."