We propose an altermagnetism-induced route to a two-dimensional higher-order topological Dirac semimetal in a trilayer nonsymmorphic Dirac system. Interlayer hybridization preserves the nonsymmorphic bulk Dirac crossings and generates helical edge states in the trilayer phase. Introducing outer-layer d-wave altermagnetic order gaps the helical edge states, while only the symmetry-protected Dirac crossing at high-symmetry point M remains gapless. The resulting phase hosts a surviving bulk Dirac point, gapped edge spectra, and corner states. An exact layer-space decomposition further reveals that these features arise from the coexistence of a gapless Dirac sector and a gapped Z2 topological sector. Our results establish altermagnetism as an effective mechanism for engineering higher-order topological Dirac semimetals in two-dimensional nonsymmorphic systems.