The two 15-year-olds relentlessly taunted Emma Bailey, 34, telling her to 'go and die' and screaming abuse at her.
The pair would also mimic Emma, who has a mental age of about 8 to 10 years old, after spotting her dancing to her favourite CDs inside her home.
Emma later told her mother Eileen: "They copy me, mum, they copy me. Why me like this mum? Why I handicapped? I don't like being handicapped."
Police were called after one of Emma's three carers who visit her flat in Stockport, Greater Manchester, compiled a report about bullying.
The two unnamed girls were later spoken to by police and agreed to meet Emma and her mother to apologise for their behaviour in exchange for not being prosecuted.
The girls attended the meeting with their families under the Government's Restorative justice scheme. Emma decided at the last minute she was too upset to attend.
A teenage boy who was part of the bullying gang wrote a letter of apology.
Emma's mother, a retired clerk in her 60s told her local paper: "Emma is a very friendly person. She likes to go out into the street talking to the children and their parents.
"But they were swearing at her and it would make her very distressed. They were throwing stones at the window and sticking their fingers up at her.
"They called her a "f****** mong" and told her to 'go and die'."
Eileen said that the girls had explained they had been drinking when they abused her.
She added: "There were three people involved but one of them moved out of the district and therefore sent a letter of apology to Emma.
"The other two people came to meet me. They were two young ladies both aged 15. One was with her foster mother and one with her grandmother. Two police officers were also present.
"When I went into the room I told the girls how nervous I was. My stomach was churning. I'm sure that they were nervous too.
"It was quite informal and friendly. They told me they had been under the influence of alcohol and they thought it was fun to torment Emma.
"I gave the grandmother and the foster mother a copy of the report that had been written by the staff and told them they really had to realise how upsetting and distressing it was and how it made Emma feel.
"They have both written to Emma. One sent her a card with an apology in and the other one has written a letter with her apology and Emma was very happy to receive those letters. It has made her a lot happier and to feel confident again."
Assistant Chief Constable Garry Shewan at Greater Manchester Police said restorative justice allows victims and crimes to meet up and resolve their problems.
He said: "We try to offer victims the opportunity whenever it is right for them. Victims get closure. They get the opportunity to ask the questions that they don't get to ask in court.
"They get to face the person who caused them the harm and broke the law. They get to ask, 'why did you choose me? Why did you break the law?' and they get to hear answers to all their questions.
"We have clear evidence that restorative justice is keeping more and more - particularly young people - out of the criminal justice system. They are learning about doing right and wrong and most importantly once they have taken part in restorative justice they don't offend again."