Cell micromanipulation is an important technique in the field of biomedical engineering. Microgrippers play a crucial role in connecting macroscopic and microscopic objects in micromanipulation systems. However, since the operated biological cells are deformable, vulnerable, and typically distributed in sizes ranging from micrometers to millimeters, it poses a huge challenge to microgripper performance. To solve this problem, this paper develops a dual-driven piezoelectric microgripper with a high displacement amplification ratio, large stroke, and parallel gripping. By adopting modular configuration, three kinds of flexure-based mechanisms, including the lever mechanism, Scott–Russell mechanism, and parallelogram mechanism are connected in series to realize three-stage amplification, which effectively makes up for the shortage of small output displacement of the piezoelectric actuator. At the same time, the use of the parallelogram mechanism also isolates the parasitic rotation movement, and realizes the parallel movement of the gripping jaws. In addition, the kinematics, statics, and dynamics models of the microgripper are established by using the pseudo-rigid body and Lagrange methods, and the key geometric parameters are also optimized. Finite element simulation and experimental tests verify the effectiveness of the developed microgripper. The results show that the developed microgripper allows an amplification ratio of 46.4, a clamping stroke of 2180 μm, and a natural frequency of 203.1 Hz. Based on the developed microgripper, the nondestructive micromanipulation of zebrafish embryos is successfully realized.