The interface deformation and liquid breakup in vapor-liquid two-phase flow are ubiquitous in natural phenomena and industrial applications, and it is crucial to understand the corresponding mechanism correctly. In this paper, the droplet and liquid ligament dynamic behaviors are investigated by simulating three benchmark cases adopting a three-dimensional phase-field-based lattice Boltzmann model, and the vapor-liquid phase interface deformation and liquid breakup mechanisms including the capillary instability and end-pinching mechanism are analyzed. The analysis results show that the capillary instability is the driving mechanism of the liquid breakup and the secondary droplet production at a large Weber number, which is different from the Rayleigh-Taylor instability and Kelvin-Helmholtz instability characterizing the vapor-liquid interface deformation. In addition, as another liquid breakup mechanism, the end-pinching mechanism, which describes the back-flow phenomenon of the liquid phase, works at each breakup point, thus resulting in capillary instability on the liquid phase structure. In essence, it is the fundamental mechanism for the liquid breakup and the immanent cause of capillary instability.