We report the first successful growth of stoichiometric hexagonal TiAs single crystals (space group P6₃/mmc) using chemical vapor transport and investigate their vibrational, electronic, topological, and magnetotransport properties. Polarized Raman spectroscopy identifies all four Raman-active phonon modes (A_1g + E_1g + 2E_2g), consistent with the hexagonal crystal symmetry. First-principles calculations reveal nontrivial band topology characterized by a symmetry indicator Z₄ = 2 and a strong topological index ν₀ = 1, together with symmetry-protected fourfold band degeneracies at the nonsymmorphic Brillouin-zone boundary. The Fermi surface exhibits an orbital-dependent crossover from quasi-two-dimensional cylindrical sheets to a corrugated three-dimensional structure along k_z. A Van Hove saddle point approximately 0.5 eV below the Fermi level along Γ--K is associated with a neck-disrupting Lifshitz transition and enhanced density of states. Magnetotransport measurements reveal a pronounced twofold angular magnetoresistance, consistent with anisotropic Fermi-surface geometry and open cyclotron orbits. Hall measurements indicate uncompensated, hole-dominated transport, accounting for the absence of extreme magnetoresistance and contributing to the field-orientation-dependent Hall response. These results establish hexagonal TiAs as a platform for exploring the interplay of nonsymmorphic band topology, Van Hove singularities, and anisotropic electronic transport in transition-metal monopnictides.