Barcelona have just relieved Ronaldo Koeman of his duties which of course means he will no longer be the manager; he has been fired/sacked. The phrase 'relieved of their duties' suggests that the employers (Barcelona's board) do not think that the manager (the employee) is good enough to hold the job so to be relieved of duties means to be let go.

Is this phrase better or worse than 'to be fired'? It is definitely worse than the phrase 'to leave the club by mutual consent' which suggests that the manager was not fired but agreed with the Board to no longer continue in their position.