The case is a fresh embarrassment over the treatment of New Zealand-born convicted criminals by Australia.
It comes as Prime Minister John Key and his Australian counterpart met in Auckland yesterday when Turnbull described the transtasman neighbours as "family".
Reacting to the Herald on Sunday story today, Mr Little said it was not how mates treated each other.
"Malcolm Turnbull yesterday said more consideration would be given to individual circumstances. Labour welcomes the Australian Prime Minister's commitment to put more resources into immigration to speed up the appeal process," Mr Little said.
"But it is more important that proper consideration is given to individual circumstances at the time visas are revoked, than appeals are processed faster."
Mr Little said New Zealand was being treated like the poor cousin by Australia.
"This is not how mates treat each other. Labour calls on the Australian Government to be realistic about people such as this man and his ability to cope in an unfamiliar country with no capacity to look after himself without the support of friends and family."
Australia's Department of Immigration and Border Protection would not comment to the Herald on Sunday last night.
Paul - who is wheelchair bound but has some feeling in his arms - said he was jailed twice after being caught self-medicating with controlled painkillers.
After the first incident in 2012 he served 13 months in jail. A few months after his release he was caught again and served a further seven months.
He was extradited last month under a controversial new Australian law which allows foreign nationals who have served a year or more in jail to be deported.
The man says he would be begging on the streets of Auckland had it not been for government-funded charity Prisoners' Aid and Rehabilitation Society (Pars).
"I feel like I've just been dumped - away from all my family and friends. I have nothing here."
Earlier complaints about the deportation system include Angela Russell who has spent 37 of her 40 years in Australia but is being sent here after being convicted of theft.
Junior Togatuki, 23, died while in a detention centre after his pleas not to be deported were rejected. He was 4 when he moved from Auckland to Sydney and told authorities he had "no memory" of New Zealand.
More than 200 New Zealanders are held in seven detention centres, including some who have lived in Australia their whole lives.
Key tried to force a backtrack on the law but Turnbull has refused to budge, saying only more resource would be poured into the appeal process to speed it up.
Turnbull said there had been a large number of revocations since the law was introduced last year but the numbers would go down as the backlog was cleared.
Paul, who broke his neck in a 2010 accident, said the deportation policy didn't take into account the severity of someone's crime.
"I'm not making excuses for what I did, but I didn't hurt anyone and I wasn't dealing anything," he said.
He was told his visa was being withdrawn by the Australian Government two days before his second jail term was up. He said he then spent an additional four months in a detention centre while his deportation was organised.
Paul's case, and that of other Kiwi deportees, is putting strain on Pars' resources, the Department of Corrections-funded service.
Tui Ah Lo, Pars' executive director, said the level of resource available to them has posed serious difficulties in trying to offer Paul the service he needs.
