This study investigates the intricate dynamics of typhoon-like vortex track deflections over complex terrain, explicitly focusing on Taiwan Island. We develop a novel dynamic model based on the conservation of potential vorticity (PV) that incorporates a topographic adjusting parameter (α) and a meridional adjusting velocity (MAV) to capture the vortex's response to terrain variations. We elucidate the fundamental mechanisms driving track sensitivity and predictability using idealized simulations and real-case scenarios that use Taiwan's topography. Our results show that steeper terrain gradients consistently deflect tracks, with this topographic steering effect amplified for stronger vortices due to their more significant α value, leading to an enhanced MAV and more pronounced deflections. Shallower impinging angles, resulting in prolonged interactions with steep terrain, further enhance these deflections. We identify distinct Track Diverging Zones (TDZs) and Track Converging Zones (TCZs) associated with Taiwan's Central Mountain Range (CMR), highlighting the significant impact of the initial position of a vortex and terrain resolution on forecast reliability. The model successfully captures the key features of vortex–topography interactions, providing a physical basis for understanding the observed variability in typhoon tracks near Taiwan. This work demonstrates the practical value of a dynamic modeling perspective and PV analysis in improving typhoon track forecasting and risk assessments in regions with complex topography. It suggests that future research should focus on refining numerical models.