John Miller, 38, used an axe and knives to carry out the frenzied attack in their family home.
After carrying out the killings, Miller told police and psychiatrists that he believed he was being brainwashed by his computer.
He also claimed he believed a nuclear war was about to start, he could see aliens from his back garden and he had made a tin foil hat for himself to block out their signals.
Miller was sentenced to 15 years today after pleading guilty to manslaughter on the grounds of diminished responsibility over the killing of partner Sarah Laycock and daughter Abigail Miller at their home in Garforth, Leeds, on January 14 last year.
It can also be revealed today that Miller, a member of the far-right British National Party, decided to spare his other daughter Amelia on the grounds that she was “a pure Aryan”. She would later be found cowering upstairs by police.
Amelia was left for at least 12 hours in the house with the bodies of her mother and sister. The court heard that the youngster has been left so terrified of her father she now asks relatives “what is the size of the padlock on daddy’s door?”
The court heard that Miller told police he carried out the killings on January 14 last year, stabbing his partner 19 times around the face, neck and chest - with one wound going through her eye.
He then hit her four times in the face with an axe.
The court heard that Abigail must have put up a considerable struggle, due to defensive injuries she suffered.
She was finally killed with a wound to the neck.
Police found Miss Laycock’s body in the kitchen and her daughter was in the living room.
The court heard that police officers who were called to the incident and who were involved in the investigation were deeply affected by what they witnessed. One officer has since resigned due to the trauma.
After leaving the house, Miller went on a violent rampage, attacking paramedics who were called to the Fairburn Ings nature reserve.
When they fled, leaving him in the ambulance, he took off his clothes and was shouting and making racist remarks when officers arrived.
Miller told police that the night before the killings, he ate with his family and said it felt like their last meal together.
He also said they watched Coronation Street together.
The judge said Miller had a “jealous and controlling” nature and was clearly a dangerous man.
He said three psychiatrists disagreed about whether Miller was a paranoid schizophrenic and should be treated in a mental hospital.
The judge said he had decided it was not appropriate to grant a hospital order in this case.
In statement read to the court, Miss Laycock’s father, Christopher, said: “I’ve had no reprieve, no release for good behaviour. My daughter and grandaughter - brutally and violently murdered - their basic human rights removed - their right to live.
“Everything I’ve worked for is now gone. Everything I planned for has gone. The lifestyle I accepted as the norm has been shattered.”
The judge said Miller had appeared to show some remorse but, in reality, his only concern was whether he could rebuild his relationship with his daughter.
There were gasps of disbelief from Miss Laycock’s family in the public gallery at this remark.
Many of the family members were already in tears.
Sentencing Miller, the judge said the events of that night were “appalling”.
He said: “To kill your partner in this way and kill your defenceless daughter were particularly heinous crimes and have to be considered against the background of jealous and controlling behaviour.”
He said that he would have sentenced Miller to life in prison with a minimum of about 32 years if he had been convicted of murder instead of manslaughter.
Miller, who was wearing a shirt and tie without a jacket, was led away showing no emotion.
After he left the dock, the judge expressed concerns about the length of time the case had taken to come to court due to delays in obtaining all the relevant medical evidence.
Miss Laycock’s family issued a statement which said: “We have had to accept that Miller could only plead guilty to manslaughter with diminished responsibility.
“His welfare and duty of care appeared to be a priority, while we have had to endure the wait for the outcome of psychiatric reports. The strain, physically, mentally and emotionally has been unbearable.
“We will never come to terms with Miller’s reasons why he killed Sarah and Abi - the graphic details are truly horrendous.”
The statement continued: “John Miller has single-handedly destroyed our lives - they will never be the same again. The hurt and pain we feel for the loss of Sarah and Abi is very, very difficult to deal with.
“No custodial sentence could ever be long enough.
“We have, as a family, tried to remain dignified throughout, while we had our hearts ripped out. Unfortunately, there is no place in the British justice system for the families of victims.
“We now have to move on and sacrifice everything for Amelia. Miller has taken so much away from us, we refuse to allow him to control our lives any more.”
Detective Superintendent Lisa Griffin, who led the inquiry, said: “John Miller killed his partner Sarah Laycock and their young daughter Abigail during an appallingly violent episode in the family home during which he inflicted terrible injuries on them.
“Their deaths have left their family and friends completely devastated and two school communities shocked and upset.
“The public may ask why it has taken so long for this case to conclude. This is entirely due to the mental health of Miller who was detained in long-term psychiatric care after the incident until such time as he was deemed fit to face the criminal justice process. The family endured this agonising time with amazing strength, courage and dignity.
“He pleaded guilty to the manslaughter charges on the grounds of diminished responsibility. Several forensic psychiatrists agree that he was acutely and seriously mentally ill at the time of the offences. He had no history of mental illness and no-one could have predicted or prevented this terrible tragedy.
“The reason why his violence was directed at those closest to him can only be attributed to Miller’s psychosis. He was delusional and out of control.
“Sarah Laycock was a loyal partner, a loving mother and a hard-working deputy headteacher. She did nothing to provoke her violent death and everything to love and protect her children. Her loss can only be described as devastating to all who had the pleasure of knowing her.”