We present a mean field theory to describe phase behaviors in mixtures of a flexible polymer and a cholesteric liquid crystal under an external magnetic or electric field. Taking into account a chiral coupling between liquid crystals under the external field, we examine twist-untwist phase transitions and phase separations in the mixtures. Depending on the strength of the external field, we predict cholesteric-paranematic (Ch+N), nematic-paranematic (N+pN), cholesteric-nematic (Ch+N) phase separations on the temperature-concentration plane. We also calculate spinodal regions, which are important in phase separation kinetics inside binodal lines.