The influences of secondary electron yield (SEY) of material on the transient and saturation characteristics of two-sided multipactor discharge in cavity are numerically investigated by using particle-in-cell and Monte-Carlo methods. The numerical results indicate that as the SEY increases, the rate of electron number increases and the average value and magnitude of steady electron number also increase. The oscillation start-time of discharge current is shortened, and the steady value of discharge current increases and tends to be saturated. Both the average value and magnitude of steady discharge power increase and tend to be saturated. Both the time-delay and pulse width of deposited power waveform increase and also tend to be saturated. Under the circumstances of higher and lower value of SEY, the physical images of electron phase space, charge density, average impact energy, average SEY, electron number and discharge current are in detail shown in particle-in-cell simulation. The results can be concluded as follows. Under the circumstances of lower value of SEY, the saturation characteristics is determined by both debunching and reverse field of space charge effects. But under the circumstances of higher value of SEY, the multipactor mechanism tends to be one-sided mode in the steady stage which can be obviously determined by reverse-field of space charge effect.