Piezoelectric-actuated micropumps have been introduced to generate small-scale flow rates of fluids for intricate applications requiring accurate and controlled flow. The performance of the micropump is basically governed by a piezoelectric actuator, the frequency of the exciting voltage a diaphragm, and the fluid type. In order to improve the micropump performance in terms of flow rate and backpressure, a diaphragm made of passive polymeric membrane reinforced by nanoclay particles which bonded to the piezo-actuator is considered and its viability examined. Both the static and the dynamic performance of the proposed micropump are investigated using a mesh-free method approach. This method is based on moving least squares (MLS) shape functions and first order shear deformation theory. The material properties of the nanoclay-reinforced composite are estimated by a two-step model consisting of an effective particle concept and Halpin–Tsai approach. The effect of the diaphragm thickness and the nanoclay volume fraction as well as the amplitude and the frequency of the exciting voltage are investigated in terms of micropump's diaphragm deflection, flow rate and pump backpressure. The results of our extensive analysis reveal that the diaphragm thickness plays an important role in the dynamic response of the newly devised micropump. Furthermore, it reveals that increasing the volume fraction of the nanoclay leads to the simultaneous increase in the backpressure and the flow rate of the micropump.