The decision came after an internal investigation done by the police department over the summer, authorities said during a news conference Tuesday.
On May 27, cellphone videos surfaced showing one police officer threatening to shoot a father as other officers pointed guns at his pregnant fiancee and their young children in the parking lot. Dravon Ames, 22, and his fiancee, Iesha Harper, 24, were later identified as the civilians in the video. They were accused of shoplifting at a Family Dollar store.
Chief Jeri Williams said Tuesday that two officers had been sent to the Disciplinary Review Board and that the board had recommended a written reprimand for the first officer and a six-week unpaid suspension for the second officer.
Williams said that she agreed on the discipline decision for the first officer, whom she said had used "inappropriate" language, but had also tried to de-escalate the situation. However, Williams said, she had differed with the board on how to discipline the second officer, Chris Meyer.
"After meeting with the officer, Chris Meyer, personally and considering all the facts of the case, I have notified him of my intention to terminate his employment," she said Tuesday. "In this case, a 240-hour suspension is just not sufficient to reverse the adverse effects of his actions on our department and our community."
She said that he was currently on administrative leave and that he did have rights to appeal her decision.
"It was difficult for both of us -- for me to make the decision and for him to take the call," Williams said.
On May 27, Phoenix officers responded to a report of a shoplifting incident at a Family Dollar store.
Officers caught up to the vehicle suspected in the shoplifting at a nearby apartment complex. That's when the incident quickly escalated and witnesses pulled out cellphones and started recording.
In one video, an officer can be heard yelling at Ames to get his hands up.
The officer, identified as Meyer, is then heard yelling at Ames, "I'm gonna put a f------- cap in your f------- head."
A second video of the incident shows Ames on the pavement outside his car with the same officer, Meyer, on top of him and placing him in handcuffs. The officer, according to the video, then yanks Ames off the ground and pushes him against a patrol vehicle before kicking Ames' legs apart, causing him to almost fall down.
"When I tell you to do something, you f------ do it!" Meyer is heard in the video yelling at Ames.
Ames responded that he was complying and then told Meyer, "I'm sorry."
Both videos showed other officers pointing guns at Ames' car, where Harper, who was pregnant, was in the backseat with her two daughters, a 1-year-old and a 4-year-old.
When the officers yelled at Harper to get out of the car, she told them, "I have two kids." One officer responds, "I don't give a s---, put your hands up."
Harper got out of the car holding her 1-year-old. An officer charged up and attempted to pull the toddler from her arms, according to the video. A neighbor intervened and agreed to take the children, which police allowed before arresting Harper.
Williams later posted the videos on Facebook and ordered an investigation. The officers involved in the incident were not wearing body cameras.
Police said that Harper's 4-year-old daughter had allegedly taken a doll from the store. No charges were filed against the couple because the store manager declined to press charges.
"We wear this badge as a symbol of our commitment to a higher standard," Williams said Tuesday. "One that won't erode the trust of those we serve or tarnish the pride that is involved with being a Phoenix police officer."
The couple is suing.
ABC News' Leah Larosa, Cherise Rudy and Bonnie McLean contributed to the reporting in this story.