Smoke generated during surgery affects tissue visibility and degrades image quality, affecting surgical decisions and limiting further image processing and analysis. Polarization is a fundamental property of light and polarization-resolved imaging has been studied and applied to general visibility restoration scenarios such as for smog or mist removal or in underwater environments. However, there is no related research or application for surgical smoke removal. Due to differences between surgical smoke and general haze scenarios, we propose an alternative imaging degradation model by redefining the form of the transmission parameters. The analysis of the propagation of polarized light interacting with the mixed medium of smoke and tissue is proposed to realize polarization-based smoke removal (visibility restoration). Theoretical analysis and observation of experimental data shows that the cross-polarized channel data generated by multiple scattering is less affected by smoke compared to the co-polarized channel. The polarization difference calculation for different color channels can estimate the model transmission parameters and reconstruct the image with restored visibility. Qualitative and quantitative comparison with alternative methods show that the polarization-based image smoke-removal method can effectively reduce the degradation of biomedical images caused by surgical smoke and partially restore the original degree of polarization of the samples.