Recently, how to prepare robust mechanical squeezed states has attracted a lot of attention [1, 2, 3]. Here, we propose two quantum optomechanical arrangements that permit the dissipation-enabled generation of steady two-mode mechanical squeezed states. In the first setup, the mechanical oscillators are placed in a two-mode optical resonator while in the second setup the mechanical oscillators are located in two coupled single-mode cavities. We show analytically that for an appropriate choice of the pump parameters, the two mechanical oscillators can be driven by cavity dissipation into a stationary two-mode squeezed vacuum, provided that mechanical damping is negligible. The effect of thermal fluctuations is also investigated in detail and shows that groundstate precooling of the oscillators is not necessary for the two-mode squeezing. These proposals can be realized in a number of optomechanical systems with current state-of-the-art experimental techniques.