The move, which it's calling a "very difficult decision", comes after an unsuccessful attempt to restore Roman baths on the site - a project that would've costed £8.7 million.
The cathedral's bid for Heritage Lottery funding was turned down.
The attempt to revitalise the ancient baths was an additional project on top of one called 'CloistersPlus', which was aiming to create a visitors' welcome centre, cafe and shop in the cathedral grounds.
This is now under review after the lottery funding rejection.
A spokesman from the Diocese of Exeter said: "Unlike other Cathedrals, Exeter does not have any large endowments or properties, and our maintenance bill alone for the building is forecast to be at least £4.2 million over the next decade.
"This year, we are facing a deficit in our operational budget of around £175,000... The Cathedral has had to take the very difficult decision of making a small number of posts redundant in order to balance the books.
"A consultation process has been commenced with the three members of staff that have been placed 'at risk' of redundancy. As we wish to avoid compulsory redundancies if possible, we have also made an offer of voluntary redundancy to all members of staff."
