Nadine Craig, who was 14 at the time, was pulled into the powerful machine and had to be freed by fellow pupils.
She received 40 stitches in an 11-inch (28 cms) wound in her neck and it was six months before she returned to Galashiels Academy in the Borders.
At Selkirk Sheriff Court, Scottish Borders Council pleaded guilty to breaches of the Health And Safety At Work Act by failing to carry out risk assessments at machines in the Craft and Design Technology classes over a period of almost three years.
The council also failed to ensure a piece of machinery, a Colchester Colt 600 lathe, had a proper guard on it.
The charge went on to say that as a consequence Miss Craig, who was then operating the lathe on November 16, 2007, was pulled towards it when a scarf she was wearing became entangled in its unguarded feedshaft, resulting in her severe injury and permanent disfigurement.
Carrie Macfarlane, senior procurator fiscal depute, said the girl had been told by another teacher the day before to remove the green-coloured scarf she habitually wore.
However, on the day of the incident, her regular teacher switched on the machine for her while she was still wearing the scarf.
She said that when the scarf became entangled in the machine and dragged her towards it, two pupils rushed to her aid.
Miss Macfarlane highlighted that no risk assessments had been carried on the machines from December 17, 2004, with the teacher telling the local authority he did not have the training or the time to do so.
She also pointed out there was a limitless fine for this type of offence.
Ranald Macpherson, acting on behalf of Scottish Borders Council, said there had been tensions between the teacher and the council over the issue of risk assessments. He added: "He was removed from classroom duties after this incident and shortly afterwards took early retirement."
Mr Macpherson said: "The nub of the case is the rotating screw and the lack of a guard. Clearly, a suitable risk assessment would have identified this risk existed."
He offered the council's apologies to Miss Craig, now 20, who was in the court's public gallery, for the "traumatic incident". But he pointed out she had not suffered any disability as a result of the accident and that a civil claim for damages was settled in December 2011 with a five figure pay-out.
Mr Macpherson said she had been off school for six months and after leaving Galashiels Academy she completed a course at Borders College before moving into employment.
Speaking in 2008, Miss Craig's father, Gavin, said: "For all that the surgeons have done a marvellous job, it is still a bad scar. She obviously has to live with that for the rest of her life."
Mr Macpherson said the authority, which has its headquarters in Newtown St Boswells, had an annual budget of £265 million and any fine would be paid from an unallocated reserve fund so services would not be affected.
Sheriff Kevin Drummond said that in view of the number of authorities to which he had been referred and to consider the submissions made to him he would defer sentence until next week.
The council will learn its fate on October 7.