The origin of ultrahigh-energy cosmic rays (UHECRs) is a long-standing mystery in astrophysics. Identifying the sources of these UHECRs, especially the nuclei component, is challenging and requires the detection of very-high-energy (VHE) gamma-rays ($\gtrsim 0.1 \rm~TeV$) and neutrinos. In this study, we have developed a numerical code that considers both nuclear and electromagnetic cascades to solve the transport equation for UHECRs and their secondaries. We focus on Centaurus A, a nearby radio galaxy that is considered a promising candidate for UHECR acceleration. Building upon observations of extended VHE gamma-ray emission from its kiloparsec-scale jet by the H.E.S.S. telescope, we investigate the interactions between UHECRs accelerated in the large-scale jet and various target photon fields, including emission from the beamed core. Our analysis includes the photodisintegration and Bethe-Heitler pair-production processes, and we provide a comprehensive assessment of the VHE gamma-ray signatures from UHECR nuclei. Our results demonstrate the potential detectability of VHE gamma-rays from UHECR nuclei by ground-based gamma-ray telescopes, particularly if the dominant composition of UHECRs consists of intermediate-mass nuclei such as oxygen.