The Spaniard led the club back into La Liga at the first time of asking after taking charge towards the end of the 2012-13 campaign.
However, the board have relieved Vasquez of his duties due to a "lack of confidence".
"The board have decided to dispense with the services of Fernando Vazquez as first-team coach," a statement read.
"The board's lack of confidence has led to the decision as this time – with pre-season yet to begin, we can still remedy this situation and develop an atmosphere of trust that is needed.
"The club want to sincerely thank Fernando Vazquez for all his work in a difficult time."
It is understood that the Turcos want to appoint a new boss by the end of the week.