A compact, rapid, and portable off-chip pneumatic control valve is significant for the miniaturization and integration of external pneumatic systems for microfluidic chips. In this work, an off-chip microvalve with a high-speed electromagnetic switch actuator and a polydimethylsiloxane (PDMS) material valve body has been designed to be easily encapsulated, simulated using MATLAB/Simulink software, and tested in a micromixer. Multi-physical coupling mathematical models are developed based on the elastic deformation force of the valve membrane, the driving force of the valve core, and the fluid force in the microchannel. Two single microvalves are used to form a three-way microvalve, which can control the air pressure in a pneumatic microchannel on the microfluidic chip. The relationship between the flow−duty cycle, the flow−pressure difference of the single electromagnetic microvalve, and the load pressure of the three-way microvalve is simulated and analyzed. Sample mixing performance controlled by the proposed off-chip three-way microvalve was tested to evaluate the pneumatic control capability, and the results show that the undertaking can fully satisfy the needs of a pneumatic microfluidic chip for most applications.