He turned it down as the Home Office expert doing it has no experience in looking for suicidal tendencies in people with autism.
Battle: Computer hacker Gary McKinnon
Janis Sharp said Asperger’s sufferer Gary, 46, turned it down as the Home Office expert doing it, Professor Thomas Fahy, has no experience in looking for suicidal tendencies in people with autism.
She said: “It is not a refusal – he had no choice. It is an impossibility because the assessor would not be able to diagnose him.”
McKinnon, 46, admits hacking into 97 US military and NASA computers using the name Solo in 2001/02 – but insists he was looking for evidence of UFOs.
His mother criticised the Government for continuing with the case when experts had warned Gary could kill himself if sent to the US to stand trial.
She said: "Gary's ordeal has gone on for far too long.
"The Home Office should accept the very clear and incontrovertible evidence provided by the country's leading psychiatric experts in this field.
"It's time to make the right decision and end Gary's torment of extradition.
"When he's fit and ready, as we have said all along, the CPS could try him in this country for his foolish acts that happened over a decade ago."
She went on: "No one has ever been extradited from America to the UK for conduct that took place in America so why is Britain extraditing British citizens to the US for actions undertaken on British soil?
"It's cruel, unnecessary, and for years has blighted not just Gary's life but mine and our family's too.
"The victims of extradition include the friends and family of those facing extradition.
"Parliament passed a motion in December for treaty change to take place as pledged pre-election by the coalition. Hopefully this will be implemented soon."
Ms Sharp added: "Gary has endured 10 years of mental trauma and has lost 10 years of his youth. We so need a good end to this.
"I'm sure that Theresa May will do what's right, and make a just and compassionate decision now and allow Gary to begin to regain some of the life he has lost."
A Home Office spokesman said: "The Home Secretary will make a decision as soon as possible.
"This is a complex case, in a complex area of the law, and a large amount of material has been submitted, some of it relatively recently.
"She needs to consider all the material carefully before making a decision."
Mark Lever, chief executive of the National Autistic Society, said: "Asperger syndrome is a complex condition and it would be impossible for anyone without specialised training to fully understand its impact.
"If Gary is forced to undergo an assessment that doesn't take account of his needs and he is consequently extradited, it could have very serious and potentially tragic ramifications."
He went on: "This situation has dragged on for over 10 years - and the stress of this in itself will undoubtedly have had a negative impact on Gary's mental health.
"The Home Secretary must urgently take the necessary steps to recognise Gary's needs."
Mr McKinnon, of Wood Green, North London, faces up to 60 years in jail if convicted.
A hearing will take place at the High Court on Tuesday.