Nonequilibrium phase transitions of vortex matter with a strong random pinning potential in layered superconductors are investigated by the three-dimensional frustrated anisotropic XY model and resistively-shunted junction dynamics at low, middle and high-temperatures, respectively. It is found that a disorder to order phase transition driven by an external current can be obtained at a low-temperature, however, a reordering configuration does not occur at a high-temperature. With the competition between thermal noise, disorder pins and current, the vortex matter can even show the reordering process twice at an intermediate temperature, giving a clear evidence of dc driven vortex lattice reorganization.