We computationally investigate the ability of a cycloidal turbine to cancel two-dimensional non-harmonic waves in deep water. A cycloidal turbine employs the same geometry as the well established Cycloidal or Voith-Schneider Propeller. It consists of a shaft and one or more hydrofoils that are attached eccentrically to the main shaft and can be independently adjusted in pitch angle as the cycloidal turbine rotates. We simulate the cycloidal turbine interaction with incoming waves by viewing the turbine as a wave generator superimposed with the incoming flow. The generated waves ideally are 180◦ out of phase and cancel the incoming wave downstream of the turbine. The upstream wave is very small as generation of single-sided waves is a characteristic of the cycloidal turbine as has been shown in prior work. The superposition of the incoming wave and generated wave is investigated in the far-field and we model the hydrofoil as a point vortex. This model has previously been used to successfully terminate regular deep water waves as well as intermediate depth water waves. We explore the ability of this model to cancel nonharmonic waves. Near complete cancellation is possible for a non-harmonic wave with components designed to match those generated by the cycloidal turbine for specified parameters. Cancellation of a specific wave component of a multi-component system is also shown. Also, step changes in the device operating parameters of circulation strength, rotation rate, and submergence depth are explored to give insight to the cycloidal turbine response characteristics and adaptability to changes in incoming waves. Based on these studies a linear, time-invarient (LTI) model is developed which captures the steady state wave frequency response. Such a model can be used for control development in future efforts to efficiently cancel more complex incoming waves.