<p>Hermiticity in quantum mechanics ensures the reality of energies, while parity-time symmetry offers an alternative route. Interestingly, in a three-level system, parity-time symmetry-breaking can lead to third-order exceptional points with distinctive topological properties. Experimentally implementing this in open quantum systems requires two well-controlled loss channels, resulting in dynamics that challenges a pure non-Hermitian description. Here we address the challenge by employing two approaches to eliminate the effects of quantum jump terms, ensuring pure non-Hermitian dynamics in a dissipative trapped ion. Based on this, we experimentally observe a parity-time symmetry-breaking-induced third-order exceptional point through non-Hermitian absorption spectroscopy. Quantum state tomography further demonstrates the coalescence of three eigenstates into a single eigenstate at the exceptional point. Finally, we identify an intrinsic third-order Liouvillian exceptional point via quench dynamics. Our experiments can be extended to observe other non-Hermitian phenomena involving multiple dissipative levels and potentially find applications in quantum information technology.</p>