The gas desorbed from the dielectric surface has a great influence on the characteristics of microwave breakdown on the vacuum side of the dielectric window. In this paper, the dielectric surface breakdown is described by using the electromagnetic particle-in-cell-Monte Carlo collision (PIC-MCC) model. The process of desorption of gas and its influence on the breakdown characteristics are studied. The simulation results show that, due to the accumulation of desorbed gas, the pressure near the dielectric surface increases in time, and the breakdown mechanism transitions from secondary electron multipactor to collision ionization. More and more electrons generated by collision ionization drift to the dielectric surface, so that the amplitude of self-organized normal electric field increases in time and sometimes points to the dielectric surface. Nevertheless, the number of secondary electrons emitted in each microwave cycle is approximately equal to the number of primary electrons. In the early and middle stages of breakdown, the attenuation of the microwave electric field near the dielectric surface is very small. However, the collision ionization causes a sharp increase in the number density of electrons, and the microwave electric field decays rapidly in the later stage of breakdown. Compared with the electromagnetic PIC-MCC simulation results, the mean energy and number of electrons obtained by the electrostatic PIC-MCC model are overestimated in the later stage of breakdown because it does not take into account the attenuation of microwave electric field. The pressure of the desorbed gas predicted by the electromagnetic PIC-MCC model is close to the measured value, when the number of gas atoms desorbed by an incident electron is taken as 0.4.