The breakup process of a charged, leaky-dielectric jet subjected to an axial perturbation is computationally analysed from the perspectives of linear and nonlinear dynamics using the arbitrary Lagrangian–Eulerian technique. The linear dynamics of the leaky-dielectric jet is quantitatively predicted by the dispersion relation from the linear stability analysis. Regarding the nonlinear dynamics, it is found that the charge relaxation is responsible for the radial compression of satellite droplets, which is validated by experiments. Two types of charge relaxations, namely, ohmic conduction and surface charge convection, define the pinching process into three breakup modes, i.e. ligament pinching, end pinching and transition pinching. In the ligament-pinching mode, the ohmic conduction dominates the jet breakup since the charge relaxes to the jet ligament instantaneously. In contrast, the surface charge convection takes effect in the end-pinching mode since the surface charge is convected to the jet end via fluid flow. When the ohmic conduction is comparable to the surface charge convection, the breakup occurs simultaneously at the end and the ligament. Finally, the influences of the perturbed wavenumber, the electric field intensity and the viscosity on the breakup mode and the local dynamics at pinch-off are comprehensively discussed.