The phenomenon of horn-like vortex in stator corner separation flow in an axial flow pump was first reported by the authors (ASME-FE, 142(7): 071208), and the associated external features were preliminarily presented. However, internal vortical characteristics, including the distributions of swirling strength, the deformation mechanism of vortex tube and the correlation with pressure fluctuation surge, are not revealed. In this paper, the newly developed vorticity decomposition approach is introduced, and thus more novel quantitative results are provided for the physics of horn-like vortex evolution. Firstly, the distributions of absolute swirling strength, relative swirling strength and Liutex spectrum are presented to outline the vortical features of the horn-like vortex fields. Secondly, the deformation mechanism of the horn-like vortex tube is revealed. It is found that the horn-like vortex spatial evolution can be described by the deformation terms (LST, LDT and LCT) controlling the Liutex transport process. These terms constantly act on the horn-like vortex tube in an almost independent way, causing its continuous deformations in the transit process. Thirdly, the quantitative correlation between horn-like vortex transit and pressure fluctuation surge is given. It is proved that periodic vortex transit can cause severe pressure fluctuation that is much larger than that induced by rotor-stator interaction. From multiple perspectives, a clearer evolution process of the horn-like vortex is outlined, which is conducive to controlling the corner separation flows and improving the stability of large-capacity & low-head pumping stations.