Jason Braham was shocked by images, published by the Sun newspaper, showing his daughter's killer William Jaggs dressed "as a 1950s housewife" while on a supervised trip outside of a secure mental health unit.
Oxford-educated Jaggs stabbed Lucy Braham, 25, some 66 times and tried to saw her body in half in the sexually-motivated attack at her home in Harrow on the Hill in September 2006.
Jaggs' plea of not guilty to murder was accepted on the grounds of diminished responsibility through mental illness and the judge sentencing at the Old Bailey in 2007 told him he was so dangerous he might never be freed.
The drug user, now 34, was sent to Broadmoor high-security hospital indefinitely after admitting Lucy Braham's manslaughter before later transferring to Littlemore mental health centre in Oxford in 2015.
The Sun's photo, splashed on the front page, showed Jaggs wearing a long floral and lacy dress and slip-on shoes, and holding a black carrier bag from a local shop, and the paper reported he had been on trips to Primark and Sainsbury's.
Mr Braham, a former art director at Harrow School, in north-west London, said: "I don't know why the guy is wearing a dress - he was a sort of show-off anyway, he might be being a narcissistic show-off as always or it may be more sinister."
The 68-year-old said he did not believe Jaggs was stable enough to be released and suggested the process had happened too quickly.
In a statement to the Press Association, he said: "We understand that on the day of the news photograph he was under escort, though this still suggests that the early stages of his potential release, during which he would have been confined to the hospital grounds, have been passed through very rapidly.
"There is no punishment on earth that would be equal to the crime that William Jaggs committed, but however long his sentence he must never be released until he has demonstrated insight into the monstrosity of what he did and shown remorse.
"Even then he could only be freed under the closest monitoring to ensure he keeps to his prescribed medication and cannot return to the illegal drugs that precipitated his psychosis."
Mr Braham said Jaggs's lack of remorse was shown in a chilling letter to a former neighbour, telling her he would "be out soon".
Jaggs had offered the woman his kitten but was turned away before he gave it to Miss Braham, who later returned it to him when she changed her mind - triggering the attack.
Mr Braham, who now runs a pottery studio in Dolau, in Powys, mid-Wales, said: "About four years ago, he wrote a letter to another of the neighbours, who happened to be a childhood friend of Lucy's.
"He had tried to deliver his cat to her first of all.
"I have not seen it (the letter) but she was very, very upset by it."
He added he was "very disappointed" he had not been kept informed about Jaggs' staged release, which he thought would be drawn out over four years or more, and had found out from a newspaper reporter.
"The system does not seem to work for letting the victim's family know what's going on," Mr Braham said.
"I would expect to have been informed of that and it was a bit of a shock.
"To Lucy's friends the news will have been a terrible shock. I'm presuming most of them had seen it on the newstand.
"We started getting phone calls from Lucy's pals, who were horrified. I'm particularly upset they've been hurt by this. I reassured them it must be part of the staged release."
In his statement, he added: "We have tried to build new lives and throughout this time we have enjoyed the support of Lucy's closest friends.
"We very much regret that these friends and so many others who knew and loved her have had to see the story of Lucy's murder re-run under new photographs of her killer, apparently walking a suburban street dressed as a 1950s housewife."
Oxford Health NHS Trust, which runs Littlemore, declined to comment on the specific case but said: "The trust works with the Ministry of Justice to help patients to safely rehabilitate and recover, including extremely careful monitoring of risk to ensure the safety of both the patient and wider public."