Yes it can be appealed because under court rules it is a final order or judgment. However, there is no right to have the appeal heard by the US Supreme Court unless that court decides to hear it.
A writ of mandamus is a court order instructing an inferior court, a corporation or a person to perform some duty specified in the order.
For an example of a writ of mandamus by an appeals court...
A mandamus is an order to a public agency or governmental body to perform an act required by law when it has neglected or refused to do so. A person may petition for a writ of mandamus when an...
This will depend on the jurisdiction, but will usually involve filing a motion for writ of mandamus with the clerk of court for whatever court you are appealing for a writ of mandamus from.
Writ of Mandamus can be filed, as per our constitution under Article 32 in the Supreme Court, and under Article 226 in the High Courts of the States.All the writs known as the constitutional remedies...