This paper presents a partially coherent point-diffraction digital holographic microscopy (PC-pDHM) prototype and demonstrates its application in label-free imaging of the dynamic processes of live cells. In PC-pDHM, the light scattered by a rotating diffuser is coupled into a multi-mode fiber, and the output light is used as the partially coherent illumination (PCI), which reduces the speckle noise significantly in PC-pDHM. A polarization-grating is used to remold the object and the reference waves, and the fringe contrast of the generated hologram can be adjusted by changing the polarization of the illumination wave. Using the PC-pDHM prototype, transparent samples and notably the dynamic processes of live cells were imaged with high contrast and in a label-free manner, discovering the pathological mechanisms of biology in the cellular and sub-cellular levels.