  We propose to mechanically control photon blockades (PB) in an optomechanical
system with driving oscillators. We show that by tuning the mechanical driving
parameters we achieve selective single-photon blockade (1PB) or two-photon
blockade (2PB) as well as simultaneous 1PB and 2PB at the same frequency. This
mechanical engineering of 1PB and 2PB can be understood from the anharmonic
energy levels due to the modulation of the mechanical driving. In contrast to
the optomechanical systems without any mechanical driving featuring PB only for
specific optical detuning, our results can be useful for achieving novel photon
sources with multi-frequency. Our work also opens up new route to mechanically
engineer quantum states exhibiting highly nonclassical photon statistics.
