Two frequency combs emitting from a single cavity are of great potential in the field of dual-comb spectroscopy because they are mutually coherent and therefore the common mode noise can be suppressed naturally. However, it is difficult to fully and flexibly control the repetition frequency difference in most of the all-optical schemes. In this paper, a birefringence-compensation Kerr resonator is proposed for the mutual dual-comb generation. It is shown that by offset aligning the fast and slow axis with appropriate fiber length, the total birefringence of the cavity can be equalized while the local one keeps at a high level. Theoretical investigations reveal that the polarization decoupled mutual dual-comb can be generated with nearly the same power level and arbitrary repetition frequency difference. Additionally, a numerical model of polarization-maintaining fiber (PMF) with near-zero dispersion is proposed for the proof of the concept. Based on this fiber, the coherent polarization-decoupled dual-comb with 10-dB bandwidth of 33 nm can be obtained. And the repetition frequency difference can be flexibly tuned compared to the cavity without offset alignment.