A method for stopping the operation of a wind turbine is disclosed. The method may generally include receiving signals associated with at least one operating condition of the wind turbine, analyzing the at least one operating condition with a controller of the wind turbine, implementing a first stopping procedure in order to stop operation of the wind turbine when analysis of the at least one operating condition indicates that a pitch system failure has occurred and implementing a second stopping procedure in order to stop operation of the wind turbine when analysis of the at least one operating condition indicates that a different wind turbine stop event has occurred.