In this paper, we propose a giant circular dichroism (CD) chiral metamirror that differentially absorbs circularly polarized (CP) waves with dual/multi bands. The structure is composed of two variable τ resonators with counter split opening directions and different eigenfrequencies. Even more important, these two resonators are aligned vertically, and then integrated into one periodical unit cell, which results in the high-efficiency absorptive CD. The chiral metamirror has a narrow-band absorption of the left-handed circularly polarized (LCP) wave for lower resonance, and a broadband absorption of the right-handed circularly polarized (RCP) wave in the higher-frequency range. Optical resonator designs with diversified chiral molecules combinations are further studied in detail. Through the study of different periodic arrangements, parameters scanning optimization, and power loss distributions, it is proved that the overall permutation symmetry breakdown of total combined chiral molecules is the determining factor for the absorptive CD. Based on the principle in the microwave model, two mid-infrared chiral metamirrors are further realized, which can still show good spin-dependent absorption. This multi-polarization and multifunction response advance novel photonic devices for a variety of applications including CP laser, biomolecules detection, and energy harvester.