Polarization sensitive MIMO radar with frequency diverse array (PSFDA-MIMO) can provide additional target polarization information. It has a better target localization, tracking, classification, and recognition performance, compared with FDA-MIMO radar. In this paper, a sparse polarization sensitive FDA-MIMO radar with co-prime frequency offsets (SPS-CopFDA-MIMO radar) is proposed and a fast parameter estimation algorithm based on propagator method is developed. In receiver, the SPS-CopFDA-MIMO radar introduces full component electromagnetic vector sensor (EMVS) spaced much farther apart than a half-wavelength to achieve aperture extension, therefore provides high accuracy and unambiguous estimates of angle and polarization. In transmitter, the SPS-CopFDA-MIMO radar utilizes co-prime frequency offsets to enhance range resolution without decreasing the maximum unambiguous range. In the proposed algorithm, the angle, polarization, and range are estimated successively. First, polarization diversity is utilized to resolve the phase ambiguity induced by the sparse receiving array. Then, the polarization parameters are estimated based on these estimated angle parameters. Finally, a two-step phase unwrapping processing is proposed to get the high resolution and unambiguous range estimates. The Cramer-Rao bounds for angle, polarization and range are derived. The performance of the proposed SPS-CopFDA-MIMO radar technique is also validated by computer simulation results.