To address the difficulty of conventional linear vibration isolators in simultaneously suppressing resonance peaks and maintaining high-frequency isolation performance, a passive piecewise damping isolator based on a translating cam mechanism is proposed and applied to passive vibration isolation under harmonic base displacement excitation. Through the geometric design of the cam profile, the isolator realizes a piecewise damping characteristic of “no damping under small displacement and damping under large displacement”. Based on the force analysis of the cam and rollers, the vertical equivalent damping coefficient of the isolator is derived, and the dynamic model of the piecewise damping passive isolation system is established. The steady-state response is solved by the averaging method and verified by Runge-Kutta numerical integration. Furthermore, the displacement transmissibility expression is derived, and the effects of cam angle, damping ratio and switching threshold on the isolation performance are analyzed. The results show that the isolator can effectively suppress the displacement transmissibility peak in the resonance region through damping activation. As the relative displacement decreases in the high-frequency region, the damping effect can be weakened or deactivated, thereby avoiding the increase in high-frequency transmissibility caused by the continuous action of linear damping and demonstrating better overall isolation performance than the linear damping system.