Bamboo-like SiC nanowires (NWs) have specific geometric shapes, which have the potential to suppress thermal conductivity by phonon boundary scattering. In this work, phonon transport behaviors in the 3C-SiC, 4H-SiC, and 6H-SiC crystal lattices are studied by the Monte Carlo (MC) method, including impurity scattering, boundary scattering, and Umklapp scattering. Phonon relaxation times for Umklapp (U) scattering for the above three SiC polytypes are calculated from the respective phonon spectra, which have not been reported in the literature. Diffuse boundary scattering and thermal rectification with different aspect ratios are also studied at different temperatures. It is found that the thermal conductivities of the bamboo-like SiC polytypes can be lowered by two orders of magnitude compared with the bulk values by contributions from boundary scattering. Compared with bamboo-like 4H-SiC and 6H-SiC NWs, 3C-SiC has the largest U scattering relaxation rate and boundary scattering rate, which leads to its lowest thermal conductivities. The thermal conductivity in the positive direction is larger than that in the negative direction because of its lower boundary scattering relaxation rate.