All three attacks happened in Manurewa, in the Counties Manukau police district, between February and April last year.
Mills resigned before he was charged in September with causing grievous bodily harm with reckless disregard, injuring with intent and common assault.
The 31-year-old has now pleaded guilty to all charges and will be sentenced in the Manukau District Court next month.
Judge Gus Andree Wiltens permanently suppressed Mills' home address after fears were raised about the safety of the former police officer.
The grievous bodily harm charge carries a maximum penalty of seven years in prison but a sentence of home detention is also possible.
However, the prosecution also raises questions about whether Mills' colleagues reported the second assault, where he kicked the restrained 15-year-old in front of fellow officers, and what action was taken.
A spokeswoman for the Counties Manukau police declined to comment as the matter was still before the courts.
Mills' barrister, Todd Simmonds, could not speak on his behalf for the same reason.
When interviewed by police investigators about the complaints, before his guilty plea, Mills said two of the three suspects were resisting arrest and force was necessary.
In regards to the third victim, the 15-year-old restrained by other officers, Mills said he ran too close to his head and accidentally stomped on him. It was not a kick, he said.
By law, police officers are allowed to use reasonable force "as may be necessary" in the execution of their duties such as arrests. Anyone, including police officers, can also use reasonable force in self-defence.
However, police policy sets out guidelines about the use of force and sets out tactical options, such as pepper spray or Tasers, which are available to officers.
Officers are trained to make judgment calls to decide whether force is necessary compared with the level of threat and risk to themselves and the public.
The policy states any force must be "timely, proportionate and appropriate given the circumstances known at the time" and every effort must be made to minimise harm. Ultimately, the legal authority to use force comes from the law, not police policy.
Police Association president Greg O'Connor said the case disproved the "myth of police going easy on their own".
"We work in a goldfish bowl. If anything like this happens, it's often reported by fellow officers, robustly investigated and put before the courts."
Abuse of power
Common assault
February 22, 2015: Mills investigates report of wilful damage at the Manurewa train station. Accuses a 15-year-old boy of the crime and tackles him, before punching him in the head several times.
Injures with intent
April 19, 2015: Fifteen-year-old boy arrested for stealing a car. He was lying face down on the road when Mills ran towards him and kicked him in the head without warning. The teenager needed medical treatment for swelling and bruising.
Causing grievous bodily harm
April 21, 2015: A 23-year-old man who stole a car was lying under a tree to avoid being found by police, but was found by the Eagle helicopter, which alerted Mills. Without warning, the officer kicked the man in the face and fractured an eye socket. The victim needs surgery.
