When a small periodic shear is applied to randomly distributed vortices, they progressively transform into an organized configuration, which is called random organization or dynamic ordering. By contrast, when the vortices with a moderately organized configuration are driven by a small dc force over a random substrate, they are gradually pinned by random pinning sites and finally reach disordered plastic flow, which is indicative of dynamic pinning or dynamic disordering. From the time-dependent voltage (i.e. average velocity), we find that random organization caused by the ac drive is suppressed with an increase in the dc drive superimposed with the ac one, and finally vanishes as the dc voltage becomes equal to the amplitude of the ac voltage in the steady state, where the vortices move in the forward direction only. The steady-state vortex configuration formed with the superimposed ac and dc drives is, in general, not uniform microscopically but comprises organized and disordered regions.