Post-arc plasma dissipation is a key process in the dielectric recovery of vacuum interrupters and is dynamically coupled to the external circuit. Hot metallic particles produced by contact erosion can release copper vapor after current zero, and collisional ionization of this vapor supplies a localized secondary plasma. A three-dimensional hybrid Maxwell-Boltzmann model with external-circuit coupling is developed to simulate particle evaporation, plasma transport, transient recovery voltage (TRV), post-arc current (PAC), and sheath expansion. Heavy species are tracked as macroparticles, whereas electrons are treated as a fluid. The plasma calculation supplies the contact-collected current to the circuit equations, and the resulting electrode charge updates the boundary conditions of the Poisson equation for the next plasma step. Calculations use a 10 mm contact gap, a copper particle with a radius of 250 μm, temperatures of 1700-1900 K, and six spatial positions. For an on-axis particle at the gap midpoint under the baseline 10 kV circuit condition, the Cu⁺ ion count falls to zero within 2.5 μs at 1700 and 1800 K. At 1900 K, however, the ion count becomes nearly constant after approximately 2.5 μs, and the PAC magnitude remains near 0.17 A after its peak. In this case, sheath expansion stagnates because ion production from the evaporated vapor balances removal by the sheath field and plasma transport. Under otherwise identical plasma conditions, imposing a linear increase in TRV magnitude at 10 kV/μs reduces the Cu⁺ ion count to zero at 3.1 μs. Within the circuit-coupled model, increasing the peak source voltage to 20 or 30 kV likewise reduces the ion count to zero within 5 μs. Particle temperature therefore mainly affects local plasma production, whereas source voltage affects field-driven removal; their balance determines whether the sheath reaches the post-arc anode. To investigate the effect of particle position, six axial and radial positions are compared at a fixed particle temperature of 1900 K, with the circuit parameters held at their baseline values. Among the three on-axis positions, the Cu⁺ ion count reaches zero within 5 μs only when the particle is 2.5 mm from the post-arc cathode. Moving the mid-gap particle radially outward increases the residual Cu⁺ ion count at 5 μs, whereas the PAC magnitude decreases from 0.167 to 0.097 A. Radial displacement also produces plasma accumulation on the outward side of the particle and asymmetric electric fields at the contacts, features that an axisymmetric model cannot represent. For the six positions examined, the PAC magnitude at 5 μs is not a monotonic indicator of the residual Cu⁺ ion count and is therefore insufficient by itself to assess plasma removal. These results highlight the importance of external-circuit coupling for capturing the interaction among particle-induced plasma production, post-arc plasma transport, and TRV evolution, and of three-dimensional spatial resolution for resolving off-axis asymmetry.