Alasdair McCrone, of Mull Theatre, and Gordon McLean, of the arts centre An Tobar, were among three directors of the umbrella body Comar.
It looks after a number of arts organisations on the island.
Comar's board said funding restrictions made it necessary to reduce three posts to one.
It said the three existing directorial posts - in theatre/dance, visual arts/film and music/literature - would be replaced by one artistic director who would lead the entire creative programme
Comar, which was created two years ago, said it hoped to continue to work with both Mr McCrone and McLean.
Equity blames poor business planning and is calling on the board to resign.
A public meeting about the decision is to be held in Tobermory next week.
High-profile Scottish actor Alan Cumming tweeted: "This makes me so sad.  Another example of the accountants take over at the expense of the art. And in Mull too."
Former Scottish culture secretary and SNP MSP for Argyll and Bute, Michael Russell, tweeted: "Making Alasdair & Gordon redundant is an extraordinary wrong-headed decision and must be opposed."
The actors' union Equity has hit out at the decision to remove two of Mull's best-known creative directors from their posts.