Altermagnets (AMs) exhibit vanishing net magnetization but strong momentum-dependent spin splitting enforced by crystal symmetry. Here, we explore the non-Hermitian (NH) effects in dissipative two-dimensional AMs. We show that symmetry-compliant dissipation naturally induces an imaginary staggered exchange field, driving an NH topological phase transition absent in conventional antiferromagnets. In the topologically nontrivial phase, hybrid skin-topological modes driven by altermagnetic $d$-wave anisotropy emerge, as captured by the chiral skin effect framework. In the gapless phase, we elucidate the creation and annihilation dynamics of exceptional points. Crucially, we analytically prove via the transfer matrix method that corner states are deterministically controlled by the boundary sublattice termination. Due to the symmetry constraints and the robustness of chiral states, these findings hold universally across all topological AMs. A general framework is established for controlling topological corner states, offering a new strategy for designing magnetic materials with tailored non-Hermitian properties.

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• Altermagnetism
• Topological phase transition
• Altermagnets
• Non-Hermitian systems
• Transfer matrix method