With the rapid development of infrastructure in western China, numerous arch bridges have been constructed as vital transportation hubs spanning river canyons. Understanding the impact of canyon topography on the seismic response of long-span half-through arch bridges crossing canyons is essential. This study first establishes a seismic input method for oblique P-wave and SV-wave incidence, based on the viscous-spring artificial boundary theory, which transforms ground motions into equivalent nodal loads on artificial boundaries. The feasibility of this proposed method is systematically validated. Subsequently, parametric investigations are carried out to explore the effects of seismic wave incidence angle, canyon depth-to-breadth ratio and soil elastic modulus on the ground motion amplification characteristics in V-shaped canyons under oblique P-wave and SV-wave excitations. Finally, dynamic response patterns of the arch ribs and the stress-strain relationships at critical structural components are thoroughly analyzed. Key findings reveal that SV-waves induce significantly different ground motion amplification effects compared to P-waves, with the wave incidence angle and canyon width-to-depth ratio being crucial influencing factors. The connection between the arch footings and the concrete cross braces constitutes the most vulnerable region, frequently exhibiting maximum stresses that exceed the yield strength of C40 concrete under multiple scenarios. Notably, when the depth-to-breadth ratio (D/B) is 0.75, the peak stress at the arch footings reaches 5.18 x 10(7)kPa, surpassing the yield stress threshold of C40 concrete. These findings highlight the need for special seismic fortification measures at these critical connections during bridge design. This research offers valuable insights into the seismic design of long-span arch bridges in complex topographic conditions.