In contrast with the optical radiation force induced by conventional lasers of continuous mono-frequency wave-fields, a dynamic or oscillatory mode arises when a beating effect caused by intensity changes over time (i.e., amplitude modulation) occurs. The purpose of this analysis is directed toward examining theoretically the dynamic (oscillatory) radiation force in optical heterodyning, caused by interfering/mixing two electromagnetic/optical plane waves driven at slightly different frequencies. The example of a dielectric cylinder material having a circular geometric cross-section is considered. Based on the integration of Maxwell's stress tensor over the surface of the object in the near-field, the modal expansion method in cylindrical coordinates is used in conjunction with the short-term time average to obtain mathematical series for the longitudinal dynamic optical radiation force per-length (i.e. acting along the direction of wave propagation). The cases of incident TM and TE polarized plane progressive waves are considered. Numerical illustrative results for the dimensionless dynamic radiation force function are performed with particular emphasis on changing the size parameter of the cylinder as well as the normalized difference-frequency and time parameters. The results show that the total force is not the mere sum of the components originated by the primary waves. There is an additional cross-term factor related to the dynamic component which cannot be neglected, suggesting that the radiation force phenomenon using beating optical waves is slowly time-varying (oscillatory). Moreover, a resonance splitting effect in the plots of the dynamic radiation force is observed and discussed. The present analysis has the potential to open a novel method in the development of dynamic/oscillatory optical heterodyne tweezers and tractor beams for particle manipulation and characterization.