We propose and realize a bandwidth and wavelength-tunable all-optical filter with high tuning efficiency based on double opto-mechanical microring resonators (MRRs) assisted Mach-Zehnder interferometer (MZI) structure, which is beneficial to achieve high extinction ratio and shape factor. As the optical field gradient is largely enhanced in the free-hanging MRRs, the opto-mechanical effect could be excited by low power consumption. By injecting the corresponding low resonance powers, the drop transmission of each MRR could be flexibly tuned based on the opto-mechanical effect. Consequently, the synthetic transmission of the microring-assisted MZI could be efficiently manipulated. The results show that by injecting pump powers of 0.40 mW and 1.84 mW, the bandwidth and wavelength of the all-optical filter could be tuned from 0.17 nm to 0.30 nm, and from 1550.09 nm to 1550.60 nm respectively with maintaining a high extinction ratio of 38 dB and a small passband ripple of 1 dB. Especially, the tuning efficiencies of bandwidth and wavelength could realize up to 0.325 nm/mW and 0.277 nm/mW, respectively. The proposed optical filter has dominant advantages of high tuning efficiencies and extinction ratios, small passband ripple and compact footprint, which has significant applications in on-chip all-optical systems.