Stephen Brisbane left his 64-year-old victim Sandra McGowan lying unconscious on her bedroom floor in Dundee.
The 34-year-old chopped off her hand, put it in a carrier bag and then put in his mum's freezer.
Minutes later it was discovered in one of the freezer drawers by his sister who phoned the police.
Victim Miss McGowan, who was in a wheelchair after suffering a stroke 14 years ago which left the left side of her body paralysed, let Brisbane into her home using a remote key fob after he knocked on her door.
Prosecutor Richard Goddard said: "She believed it was later and believed it was her carer who usually arrived first thing in the morning.
"She used a remote controlled electronic key fob to open the door as she lay in bed.
"The accused walked up, gave her a cuddle, told her his name was Stephen and offered to make her a cup of tea."
Ms McGowan could hear cupboards opening and closing in the kitchen and moved herself into her wheelchair and found the accused looking in her freezer.
She had her back to Brisbane who had grabbed a knife before taking hold of her. There was a brief struggle and she fell from her wheelchair.
Mr Goddard said: "As she fell her right arm was raised and Brisbane seized her right wrist. She saw he had a knife in his hand. He then started to cut her right wrist and she lost consciousness.
"Around two hours later she regained consciousness and saw her right hand was gone."
The court heard she tried to get up from the floor by putting her feet under the bed, but was only able to get to a seated position. She called for help, but no one heard her cries.
When her carer and a district nurse arrived they were unable to get into the house and called the police. They forced their way into the bungalow and found Ms McGowan in her bedroom. She was covered in blood and so was the room.
A seven-hour operation to try to reattach the hand was performed, without success.
Mr Goddard said: "She was previously able to feed herself, shop for herself, live by herself and enjoy independence. She routinely attended clubs and met friends. She is now unable to do any of these things unassisted. She is now in a care home and requires 24-hour assistance.
Defence QC Mark Stewart said: "He thought he was suffering from a serious illness and said he had been advised by Barrack Obama to take crystal meth. He had been told it was the cure for his illness and could be extracted from the bones of human beings."