We investigate the generation of squeezed states in a movable mirror in dissipative optomechanics in which the oscillating mirror modulates both the resonance frequency and the linewidth of the cavity mode. Via feeding broadband squeezed-vacuum light accompanying a coherent driving laser field into the cavity, the master equation for the cavity-mirror system is derived by following the general reservoir theory. When the mirror is weakly coupled to the cavity mode, we find that the driven cavity field can effectively perform as a squeezed-vacuum reservoir for the movable mirror via utilizing th...