The inductive pulsed plasma thruster (IPPT) is a sort of spacecraft propulsion device. To promote the development of IPPTs, the working process and performance influencing factors are investigated in this study, using a novel magnetohydrodynamic model, with an exterior circuit coupled and extended magnetic field involved in the computation.By exploring the spatial distributions of different physical fields and the global properties of the thruster, a comprehensive physical picture of the operation process is illustrated, which is comprised of the structure evolution of the plasma current sheet, the relationship between thrust force and circuit current, the coupling effect that derives from plasma back to the circuit, and the energy deposition and conversion process of the system. Besides, the positive contribution of the secondary current sheet to the ultimate thrust performance is also confirmed.Further investigations discuss the impacts of varied factors including the operating parameters, initial gas distributions, and metal structures nearby. The results indicate that by adjusting propellant mass to achieve identical specific energy, the specific impulse and efficiency of the thruster can remain almost constant under varied discharge energy. Both compressing the initial gas against the face of coil, and ameliorating its radial uniformity, can help enhance the coupling between the plasma and drive-coil. Conductive structures nearby, especially the grounded metal plate that mounts the capacitors, can impair the acceleration of the plasma, unless it is located out of the electromagnetic coupling distance of the drive-coil.This study may help to reveal the underlying physical mechanisms and improve the designs of IPPTs.