In this paper, a taut wire mooring system has been designed consisting of three wire ropes symmetrically arranged. The power take-off system is modelled by a linear spring and a heave plate to simulate the linear damping of the power take-off. A series of regular wave tests in head seas are performed to study the dynamics of the system. Irregular wave tests were then conducted to simulate the system performance in the operational sea states, where the irregular waves are modelled by the Jonswap spectrum. The WEC motion responses and mooring tensions are studied. The short term mooring fatigue damage estimated by different spectral methods are compared to the rainflow counting method. The spectral method for estimating fatigue damage include the Dirlik formula, Jiao-Moan method and Tovo-Benasciutti approach. The accuracy of spectral methods for predicting mooring fatigue damage are discussed.