This paper investigates a novel concept of using cycloidal propellers to augment the maneuverability of unmanned underwater vehicles. Cycloidal propellers are cross-flow propellers that utilize 360$^{\circ}$ thrust vectoring to provide agile maneuvering to surface vessels like yachts, tug boats, buoy tenders and double ended ferries, but have yet to be utilized on present-day unmanned and autonomous marine vehicles. Through 360$^{\circ}$ thrust vectoring, cycloidal propellers enable surface vessels to execute spot turns, and surge in forward and backward directions with equal ease. Such compact maneuvers are difficult to execute with the conventional screw propeller-rudder setup found on marine vehicles today. On unmanned and autonomous marine vehicles, cycloidal propellers can potentially enable controlled and decoupled maneuvering in all six degrees-of-freedom while overcoming disturbances like waves and currents, and extreme flow conditions like cavitation and ventilation. This is critical for marine vehicles operating at low speeds and in restricted waters. Therefore, the objective of this paper is to study the maneuvering characteristics of a UUV driven by a screw propeller and control fins only, and compare it to that of the UUV augmented with retractable cycloidal propellers. The cases considered are a turning circle maneuver, a low-speed 180$^{\circ}$ turn and a low-speed heave maneuver. A six degrees-of-freedom motion prediction model that accounts for the non-linear and coupled loads on an underwater vehicle is developed and validated. Simulation results showed that compared to conventional propulsion systems, cycloidal propellers could potentially enable more swift, compact and decoupled maneuvers in unmanned marine vehicles. Integrated with robust control systems, cycloidal propellers can be explored for use in dynamic positioning, ocean exploration, station-keeping, seakeeping and teaming of unmanned and autonomous marine vehicles.