Bosses at the health board aim to get rid of 1,300 posts to plug the hole in its finances, official papers revealed.
They say they can do that over several years through “natural staff turnover”, but it is feared cuts to backroom staffing will have an impact on patients.
The decision to shrink the workforce comes as the board benefits from having at least £62 million of debt written off by the Scottish Government.
The plans are revealed in an assurance report to the board from September.
It said there was an “acceptance that staff levels need to reduce by 10%”.
Gillian Murray, who has been campaigning for better mental health services after failings in the care of her late uncle, said the decision shows that “balancing the books obviously means more to them than saving lives”.
“People in Dundee are dying because NHS Tayside is a shambles and to cut the workforce is another slap in the face for all of us,” she added.
Murdo Fraser, the Conservative MSP in Perthshire, said: “Local people will be wondering what impact these massive reductions in staff will have on their already pressured services.”
Annie Ingram, NHS Tayside director of workforce, said no one will lose their job but said spending on the workforce is higher than health boards of a similar size.
She added: “We are carrying out a review of staff numbers, grades and skills, which is being carried out in partnership with our staff and our trades unions, to ensure we have a safe, affordable and sustainable workforce.”