Cardiff University has announced plans to cut 380 posts over five years as part of moves to address a budget deficit of more than £20m.
In an email to staff, university bosses said compulsory redundancies could not be ruled out but hoped the reduction could be achieved through voluntary severance and recruitment controls.
Its document Transforming Cardiff also proposes changes to departments.
Unison said it would "inevitably harm the quality of student provision".
The plans were approved by the university's governing body on Monday.
It comes after the university posted a £22.8m deficit in 2017-18, when expenditure increased by 5.2% but income only rose by 2.5%.
Its aim is to get back into surplus by 2019-20 and it wants to cut staffing costs from 59.6% of total income to no more than 56% of income by 2022-23.
"The university plans to reduce current staff levels by 7%, or 380 full-time equivalent over five years," said vice chancellor Colin Riordan in an email to staff.
"This is manageable when compared to an average annual voluntary staff turnover of more than 6%."
He described Transforming Cardiff as a programme for change that "allows us to align financial imperatives with innovative ways of delivering teaching, research and our civic mission".
Proposals include new courses in "areas of global challenges that really matter to Wales", such as data science and environmental science.
There are also plans for a new School of Literatures, Languages and Creative Practice.
But the university also wants to reduce the current campus footprint and associated rent and utilities costs and reconfigure its School of Healthcare Sciences.
The Cardiff branch of the University and College Union called on members to vote for strike action, in part to "fight compulsory redundancies when they come".
More reasons to vote #YesYes to action in our 2 active strike ballots, folks:— Cardiff Uni UCU (@CardiffUCU) February 12, 2019
1. In the local one, to fight compulsory redundancies when they come; &
2. Against pay inequality in the national one (VC pay‘s part of that, as is the gender pay gap, stagnating wages & casualisation). https://t.co/pE4haRqTLo
Katie Hall, Unison Cardiff university branch secretary, said they were concerned the number of job cuts announced would "inevitably harm the quality of student provision at Cardiff university".
"There is a lack of transparency and we don't believe the university is giving the trade unions the full story.
"University support staff work as hard as they can to make Cardiff a success. They are absolutely critical to the performance of the institution and we will completely oppose compulsory redundancies."
Analysis by BBC Wales education correspondent Bethan Lewis
Almost all of Wales's universities have been looking closely at their finances and making decisions about "restructuring".
Bangor University and the University of Wales Trinity St David are the most recent to look at savings - and other universities over the border have been struggling too.
There are some common concerns, including the lower level of grant money universities are receiving from government as they wait for welcome changes to student finance to work through the system.
Fierce competition for students is another common thread, but as Wales's highest profile university, Cardiff should be better placed than most to keep attracting applicants.
However unions claim the situation is a symptom of bad management and question how a top university found itself £23m in the red.