We present a study for the static and dynamic performance of piezo-actuated diaphragm pumps, equipped with capillary micropipettes with small orifices. The micropipettes are used for the manipulation of individual microparticles and bacteria cells. These pumps aspirate and dispense volumes of fluid between 500 pL and 250 nL at flow rates up to 250 nL/s. When a pump is equipped with a capillary micropipette of a small orifice diameter, the fluidic resistance increases causing a delayed response that increases the risk of losing the manipulated particle. A mathematical model of the pump was developed, where the effect of the diaphragm stiffness on the pump transient response and volumetric displacement were investigated. The diaphragm stiffness is represented by its material and thickness. The response time decreases with the increase of the diaphragm thickness or the diaphragm material modulus of elasticity. However, a stiffer diaphragm causes a decrease in the maximum fluidic volume the pump can displace.