David Dowson, 26, previously pleaded guilty to attempting to murder Pc Josh McCorry by striking him with the weapon outside his home in Wishaw, North Lanarkshire, in June last year.
He was originally charged with attempting to murder both officers but his plea was accepted to the lesser charge of assaulting Pc Glenn Coletta to his severe injury, permanent disfigurement and danger of life.
Pc McCorry, who was 23 at the time of the attack, had the tip of his right thumb sliced off and suffered a 3cm cut to the top of his head.
Pc Coletta required surgery to a severe injury to his right hand, which has left scarring.
Dowson was given an extended sentence comprising seven-and-a-half years in prison followed by two years under supervision when he is released, when he appeared at the High Court in Glasgow on Friday.
Judge Lady Stacey said: “You have pled guilty to very serious charges and your behaviour that day can only be described as outrageous.
“The police were dealing with a young child being returned to his home and you decided to interfere with that. You proceeded to threaten these police officers and then attack them.
“That sort of behaviour just cannot be tolerated. What you did had consequences, these police officers suffered injuries. Nobody carrying out their duties should be subjected to the sort of behaviour that you carried out that day.
“You had a meat cleaver and you had it in preparation apparently, because it was conveniently near your front door. That sort of behaviour can only be described as outrageous and it cannot be tolerated.”
Lady Stacey said Dowson has a “shocking” record of previous convictions, including a High Court conviction for assault.
She said she believes Dowson presents a danger to the public and imposed an extended sentence to ensure he is supervised for a time on his release from jail.
At the previous hearing last month, the court heard the officers were “terrified and feared for their lives” during the assault.
Advocate depute Margaret Barr said Dowson shouted: “Aye I chopped your cops up with a cleaver,” as he was put in a police van following the attack.
She said the two officers were on duty and were returning a child to the block of flats where Dowson lived in Greenfield Drive at around 10.10pm on June 14 2020, but this matter was not related to him.
As they struggled to enter the secure close, Dowson approached them and said he would take the child since he knew him, before telling the officers: “I’ll put holes in both of you.”
He was warned about his behaviour and allowed Pc Coletta, aged 24 at the time, access to the close before pulling out the meat cleaver, raising it over his head and swinging at the officer’s face.
Pc Coletta blocked the blow with his hand, and was severely injured.
Ms Barr said Pc McCorry then entered the close and Dowson punched him and then brought the cleaver down full force towards his head, causing him to fall into the wall and then the ground.
He kept swinging the weapon at the officer, making contact at least once.
One officer managed to escape through the door while the other jumped out a window to get away.
Reinforcements arrived and Dowson complied when he was told to lie on the ground, before being handcuffed and placed in a police van.
Defence lawyer Tony Graham QC said Dowson has “a distrust of those around him in society”.
He said there was nothing to say in mitigation of the incident itself but that Dowson had requested help from psychological services to address his past issues while in custody.