Mooring systems for floating wave energy converters (WECs) are a major cost driver. Failure of mooring systems often occurs due to extreme loads. This paper introduces an extrapolation method for extreme response which accounts for the control system of a WEC that controls the loads onto the structure and the harvested power of the device as well as the fact that extreme loads may occur during operation and not at extreme wave states when the device is in storm protection mode. The extrapolation method is based on short-term load time series and applied to a case study where up-scaled surge load measurements from lab-scaled WEPTOS WEC are taken. Different catenary anchor leg mooring (CALM) systems as well as single anchor leg mooring (SALM) mooring systems are implemented for a dynamic simulation with different number of mooring lines. Extreme tension loads with a return period of 50 years are assessed for the hawser as well as at the different mooring lines. Furthermore, the extreme load impact given failure of one mooring line is assessed and compared with extreme loads given no system failure.