A scheme is proposed to investigate the non-classical states generated by quantum scissors device (QSD) operating on the the cavity mode of optomechanical system. When the catalytic QSD acting on the cavity mode of optomechanical system, the resulting state contains only the vacuum, single-photon and two-photon states depending upon the coupling parameter of optomechanical system as well as the transmission coefficients of beam splitters. Especially, the output state is just a class of multicomponent cat state truncations at time t = 2π by choosing the appropriate value of coupling parameter. We have discussed the success probability of such state and the fidelity between the output state and input state via QSD. Then the linear entropy is used to investigate the entanglement between the two subsystems, which finds that QSD operation can enhance their entanglement degree. Further-more, we also derive the analytical expression of Wigner function (WF) for the cavity mode via QSD and numerically discuss the WF distribution in phase space at time t = 2π. These results show that the high non-classicality of output state can always be achieved by modulating the coupling parameter of optomechanical system as well as the transmittance of beam splitters.