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This paper presents a Monte Carlo model to investigate the single-surface multipactor discharge on a dielectric surface in the presence of RF and dc electric fields. By employing a novel method in the numerical implementation of the secondary-electron emission, the susceptibility diagram is constructed, and beam loading and its power absorption by the multipactor discharge are examined. Meanwhile, the temporal evolution of the multipactor is also studied. The simulation results show clearly that a steady-state multipactor discharge can be built up from a very low density initial electron distribution, and an oscillatory steady state can be achieved when the positive charge, which is left by the emission of secondary electrons, is capable to build a large-enough dc electric field. During the saturation state, the normal electric field and the number of electrons in flight oscillate at twice the RF frequency. The average power absorbed by the multipactor, strongly depending on material parameters, is on the order of 1% incident power or less. Based on this model, several useful guidelines to prevent or extinguish the multipactor are presented.