The interplay between altermagnetism and crystalline band topology provides an intriguing avenue for realizing unconventional topological phases with distinctive spin-dependent properties. Here, based on first-principles calculations and theoretical analysis, we identify monolayer Tc₂X₂O (X = Cl, Br) as a family of two-dimensional altermagnetic mirror Chern insulators. In the absence of spin–orbit coupling (SOC), both monolayers exhibit robust altermagnetism with mirror-spin coupling and host two symmetry-protected Weyl points in each spin channel near the Fermi level. The Weyl points in opposite spin channels carry distinct mirror-symmetry eigenvalues, m_z=± i. Upon inclusion of SOC, the Weyl points are gapped, and the two mirror sectors acquire opposite Chern numbers, cal C₊=1 and cal C₋=-1, resulting in a nonzero mirror Chern number cal Cₘ=1. A low-energy k· p model captures the symmetry protection of the Weyl points and elucidates their SOC-induced mass gaps and topological character. Furthermore, the resulting mirror Chern insulating phases host helical edge states within the bulk band gap and exhibit a quantized spin Hall conductivity. Our work establishes a direct connection between altermagnetism and mirror Chern topology and provides a promising platform for exploring unconventional topological and spin-dependent phenomena in two-dimensional altermagnetic materials.