Usually when optically pumped, dye-doped cholesteric liquid crystal (CLC) laser generates circularly polarized laser light in the same handedness as the cholesteric helix. On a distributed feedback basis, laser light at photonic band edge comes out from both sides symmetrically. In this work, we incorporated a metallic mirror reflector to the CLC laser on one side so that laser light only emits from single direction and hence the extracted output can be enhanced by ~2-5X. Furthermore, upon reflection the mirror reflector introduces a π phase change. Therefore, two different types of CLC lasers with different polarization states are demonstrated by putting the mirror at different substrates. With a mirror attached at the outer side of the liquid crystal substrate, we obtained a nearly unpolarized CLC laser based on incoherent supposition of two orthogonal circularly polarized beams. With mirror coated at one of the inner surfaces of the liquid crystal cell, we obtained a linearly polarized CLC laser based on coherent combination of two orthogonal circularly polarized beams. For these two cases, the output power and polarization states are compared and the physical mechanism is discussed correspondingly. Moreover, the tuning of the linear polarization direction is demonstrated.