Utilizing the dynamic amidation and aza-Michael addition chemistry, a set of high strength, recyclable, and self-healable covalent adaptable networks (CANs) are synthesized by reacting the precursor and commercial oligoamine cross-linkers under mild temperature (25–50 °C) and solvent-free conditions. The amide linkages present in these CANs are readily hydrolyzable under mild acidic (pH = 5.3) conditions, whereas the aza-Michael adducts with secondary amines are thermally reversible. Utilizing the above, these CANs are depolymerized under ambient conditions in mild acidic solution and recycled with retention of original mechanical properties. The crack on the material surface is self-healed at 50 °C. The precursor, a Knoevenagel condensation product of terephthalaldehyde and diethyl malonate, is easily synthesized in a large scale. Suitable model compounds are synthesized and studied to further understand the transformations involved in the polymerization–depolymerization of these networks. These networks exhibit adequate tensile properties (ultimate tensile strength ≤35 MPa and Young’s modulus ≤3 GPa), and the properties can be tuned further by suitably changing the oligoamine cross-linker. The simplicity of synthesis, cost effectiveness, adequate mechanical property, stability in aqueous and organic media, and recyclability along with self-healability render these CANs suitable for a range of applications.