High harmonic generation (HHG) by two-color counter-rotating relativistic laser pulses with arbitrary frequency ratio is investigated through particle-in-cell simulations.It is shown that the dichromatic laser driver at various frequency ratios can effectively produce high-order harmonics with different spectral features.A general selection rule of this extended scheme can be obtained and the corresponding harmonic helicity can be identified through a simple analytical model based on a relativistic oscillating mirror.Thus,the results in this paper may offer new opportunities for arbitrary spectral control of generated harmonics,which is of significance for diverse potential applications in practice.