This paper investigates the disentangling transition in topological orders induced by boundary decoherence. The study focuses on the toric code in 2, 3, and 4 spatial dimensions, analyzing how boundary decoherence affects the entanglement structure and topological order. The key insight is the connection between the negativity spectrum of decohered mixed states and emergent symmetry-protected topological (SPT) orders under certain symmetry-preserving perturbations. This allows for the analytical computation of entanglement negativity without using a replica trick. The paper explores the entanglement structure of topological orders under decoherence on the bipartition boundary. It shows that boundary decoherence can induce a disentangling transition, characterized by the destruction of long-range entanglement across the interface, measured by topological entanglement negativity. The study uses topological entanglement negativity, a subleading contribution of entanglement negativity, to diagnose long-range entanglement and characterize the disentangling transition. For the 2d toric code, the entanglement negativity relates to the free energy of the 1d Ising model. The topological entanglement negativity remains non-zero for any non-maximal noise rate, becoming zero only at maximal decoherence. For the 3d toric code, the entanglement negativity relates to the 2d Ising model, which exhibits a finite-temperature transition, indicating a disentangling transition at a critical decoherence strength. For the 4d toric code, the entanglement negativity relates to the 3d Ising model, which exhibits a confinement-deconfinement transition, indicating a disentangling transition at a critical decoherence strength. The paper also discusses the connection between the disentangling transition and the SPT-order transition, showing that both are described by the 2d Ising universality at distinct critical temperatures. The results demonstrate that the entanglement structure of topological orders can be understood through the negativity spectrum, which corresponds to the wave functions of SPT orders in lower dimensions. The study provides exact results for the negativity spectrum and entanglement structure of topological orders under boundary decoherence, offering insights into the behavior of mixed-state topological orders and their transitions.This paper investigates the disentangling transition in topological orders induced by boundary decoherence. The study focuses on the toric code in 2, 3, and 4 spatial dimensions, analyzing how boundary decoherence affects the entanglement structure and topological order. The key insight is the connection between the negativity spectrum of decohered mixed states and emergent symmetry-protected topological (SPT) orders under certain symmetry-preserving perturbations. This allows for the analytical computation of entanglement negativity without using a replica trick. The paper explores the entanglement structure of topological orders under decoherence on the bipartition boundary. It shows that boundary decoherence can induce a disentangling transition, characterized by the destruction of long-range entanglement across the interface, measured by topological entanglement negativity. The study uses topological entanglement negativity, a subleading contribution of entanglement negativity, to diagnose long-range entanglement and characterize the disentangling transition. For the 2d toric code, the entanglement negativity relates to the free energy of the 1d Ising model. The topological entanglement negativity remains non-zero for any non-maximal noise rate, becoming zero only at maximal decoherence. For the 3d toric code, the entanglement negativity relates to the 2d Ising model, which exhibits a finite-temperature transition, indicating a disentangling transition at a critical decoherence strength. For the 4d toric code, the entanglement negativity relates to the 3d Ising model, which exhibits a confinement-deconfinement transition, indicating a disentangling transition at a critical decoherence strength. The paper also discusses the connection between the disentangling transition and the SPT-order transition, showing that both are described by the 2d Ising universality at distinct critical temperatures. The results demonstrate that the entanglement structure of topological orders can be understood through the negativity spectrum, which corresponds to the wave functions of SPT orders in lower dimensions. The study provides exact results for the negativity spectrum and entanglement structure of topological orders under boundary decoherence, offering insights into the behavior of mixed-state topological orders and their transitions.