  In a weakly compressible high-$\beta$ medium, pitch-angle scattering and the
associated scattering acceleration of cosmic rays (CRs) by anisotropic
Alfv\'{e}n and slow modes of magnetohydrodynamic (MHD) turbulence is
inefficient. To tap the energy from magnetic compressions for efficient
particle acceleration, a diffusion mechanism that can effectively confine
particles in space without causing their trapping or pitch-angle isotropization
is needed. We find that the mirror diffusion in MHD turbulence recently
identified in Lazarian and Xu (2021) satisfies all the above conditions and
serves as a promising diffusion mechanism for efficient acceleration of CRs via
their stochastic non-resonant interactions with magnetic
compressions/expansions. The resulting mirror acceleration is dominated by the
slow-mode eddies with their lifetime comparable to the mirror diffusion time of
CRs. Consequently, we find that the acceleration time of mirror acceleration is
independent of the spatial diffusion coefficient of CRs. The mirror
acceleration brings new life for the particle acceleration in a weakly
compressible/incompressible medium and has important implications for studying
CR re-acceleration in the high-$\beta$ intracluster medium.
