Please see my explanation at the following link: http://www.foxappeals.com/attorney res a few words on writs.htm

A writ of mandate is a court order, generally issued in one of two circumstances: 1) From a higher court to a lower court while a case is pending in the lower court. Instead of waiting for a final judgment at the end of the case and then appealing, a party who is aggrieved by a court's nonappealable order while a case is pending can apply to a higher court for a writ of mandate; 2) A writ of "administrative mandate" can issue from a court in order to review the decision of an administrative agency: for example, someone gets a DUI, the DMV suspends his license after an administrative hearing, and the person then applies to the Superior Court for a writ of administrative mandate to have the DMV hearing officer's case reversed. In both types of cases writs of mandate are rarely granted. If a petition for a writ of mandate is denied, the party who sought the writ can usually apply to a higher court for a writ of mandate, in effect appealing the lower court's decision denying the writ.

A writ of mandate is a court order to a lower tribunal to either do something or refrain from doing something. The procedure to get a writ of mandate is a petition for a writ of mandate. What was denied was the petition, not the writ. If a writ had actually been issued, the lower tribunal would have had to follow it. Petitions for writs of mandate are used when the order being challenged is not itself appealable.