Clarifying the deformation behaviors of microstructures could greatly help us understand the precipitation-strengthening mechanism in alloys. However, it is still a formidable challenge to study the slow plastic deformation of alloys at the atomic scale. In this work, the phase-field crystal method was used to investigate the interactions between precipitates, grain boundary, and dislocation during the deformation processes at different degrees of lattice misfits and strain rates. The results demonstrate that the pinning effect of precipitates becomes increasingly strong with the increase of lattice misfit at relatively slow deformation with a strain rate of 10 -4 . The cut regimen prevails under the interaction between coherent precipitates and dislocations. In the case of a large lattice misfit of 19.3%, the dislocations tend to move toward the incoherent phase interface and are absorbed. The deformation behavior of the precipitate-matrix phase interface was also investigated. Collaborative deformation is observed in coherent and semi-coherent interfaces, while incoherent precipitate deforms independently of the matrix grains. The faster deformations (strain rate is 10 -2 ) with different lattice misfits all are characterized by the generation of a large number of dislocations and vacancies. The results contribute to important insights into the fundamental issue about how the microstructures of precipitation-strengthening alloys deform collaboratively or independently under different lattice misfits and deformation rates.