Based on the NCEP/NCAR daily reanalysis data during 1958-2017, this study comparatively analyzed the stratospheric and tropospheric evolutions during the life cycle of both strong and weak stratosphere polar vortex events (i.e., SPV and WPV events). And the atmospheric circulation and dynamical characteristics of two types of WPV events, namely with and without SSW, are also analyzed. The results showed that the formation of SPV events experienced a slow development, then a rapid intensification stage, while the WPV events are established dramatically. Compared to the SPV events, the WPV events are stronger with a higher anomaly center when they reach a peak. Moreover, the occurrence of SPV and WPV events is closely related to the positive feedback of wave-mean flow interaction. For the SPV events, a PNA-like pattern weakens the wave-1 of planetary waves during the growth stage. When the stratospheric westerly winds are strengthened to a certain extent, upward propagating planetary waves are greatly suppressed, thus the polar vortex is intensified rapidly and reaches the peak stage. For the WPV events, a wave-1 pattern enhances the upward propagating planetary waves in the growth stage, which leads to weak westerly winds soon in the stratosphere by exerting a drag on the zonal flow. More planetary waves then propagate into the stratosphere, and thus the polar vortex is dramatically weakened and even broken down. In addition, for the WPV events with SSW, enhanced upward wave-1 EP flux in the stratosphere occurres in the growth stage. Through the positive feedback of wave-mean flow interaction, both the upward propagating wave-1 and wave-2 EP fluxes are increased, which lead to the breakdown of the polar vortex. For the WPV events without SSW, the upward propagating wave-1 EP flux is weak in the growth stage, while the wave-2 flux plays an important role. Hence, the total upward propagating planetary waves are much smaller than the WPV events with SSW. For the WPV events without SSW, an EU-like pattern in the height field appears in the upper troposphere during the growth and peak stages, accompanied by strong anomalous poleward EP flux, which lead to an extremely negative AO in the troposphere. For the WPV events with SSW, a wave train from the lower latitude over the North Pacific in the height field appears in the upper troposphere mainly during the growth stage. In the later stages, the tropospheric influence of the WPV events with SSW is relatively delayed and not robust, and the magnitude of AO index is much smaller than that for the WPV events without SSW.