Mr Keen, 54, suffered horrific injuries as he used the saw to cut wood for a cabinet he was making in his home workshop.
He rang the emergency services operator and said: "Help me – I'm bleeding to death."
Police and ambulance crews rushed to his home in Wantage, Oxfordshire and found Mr Keen and the severed penis in the bath.
He was taken by ambulance to the John Radcliffe Hospital in Oxford in a serious but not life-threatening condition.
Surgeons managed to reattach the organ and yesterday doctors said he was in a "stable condition".
It is thought he had been carrying out DIY while drunk, but it was unclear whether the incident was an accident or a deliberate act.
His mother Edna, 84, said: "Stuart had a very nasty accident with a saw but he is recovering now.
"He suffered tissue damage and had surgery to stitch him up which, I understand, was successful.
"I have spoken to him and he is quite embarrassed about the whole incident. I was in Somerset when it happened and got a call from the hospital.
"Hopefully he will be home next week and be able to get back to work which he loves.
"Stuart is a carpenter and uses sharp and sometimes dangerous tools.
"This was an unfortunate accident but these things happen all the time to people in his profession."
A spokesman for the South Central Ambulance Service said paramedics had waited for police support because the patient was drunk and a sharp blade had been used.
A hospital spokesman said the man remained in a stable condition after surgeons had carried out an operation to reattach the penis.
In December 2000, a 32-year-old man walked into a chip shop in Edinburgh carrying his penis, which he had just cut off.
"There wasn't time to think about it and I shouted for the girl in the shop to get me some of the polythene bags we put the rolls in," said fish fryer Adam Harrughty at the Mermaid on Leith Walk,
The man, who had also stabbed himself in the neck, was taken to Edinburgh Royal Infirmary and then transferred to St John's Hospital in Livingston for plastic surgery.
In 1998, a 54-year-old cut off his penis with a kitchen knife at his home in the Scarborough area. He told police he had decided to take such drastic action because his penis was affected by a "very painful" medical condition.
Whatever ,penis reattachments will never feel the same. He will regret this one. talk about a little numbness. there is not one fucking nerve on that willy. It's worthless. He might as well just have a little mound with a pimple to pee out of. lol like dogma