Topological phases of matter offer a promising platform for quantum computation and quantum error correction. Nevertheless, unlike its counterpart in pure states, descriptions of topological order in mixed states remain relatively underexplored. Our study gives various equivalent definitions for replica topological order in mixed states. Similar to the replica trick, our definitions also involve n copies of density matrices of the mixed state. Using our framework, we can categorize topological orders in mixed states as either quantum, classical, or trivial, depending on which type of information they encode. For the case of the toric code model in the presence of decoherence, we associate for each phase a quantum channel and describes the structure of the code space. We show that in the quantum-topological phase, there exists a postselection-based error correction protocol that recovers the quantum information, while in the classical-topological phase, the quantum information has decohere and cannot be fully recovered. We accomplish this by describing the mixed state as a projected entangled pairs state (PEPS) and identifying the symmetry-protected topological order of its boundary state to the bulk topology.