Disassembly is one of the essential operations in manufacturing to recover the useful parts of the product after End of Life (EOL). Moreover, by generating an optimal disassembly sequence, the time to dismantle the product will be reduced, and in turn, cost also reduces. However, achieving an optimal disassembly sequence is not an easy task as it is an NP-hard combinatorial problem. Many researchers followed different approaches like mathematical, knowledge-based and artificial intelligence (AI)-based methods to generate optimal disassembly sequences. Most of the researchers concentrate on generating the optimal disassembly sequence, but only a few of them discuss the disposal of the parts after EOL. It is very much essential to consider the type of disposal that has to follow the individual components after dismantle to reduce the effect on the environment due to parts of the EOL product. In this research work, a stability graph cut-set method is applied to generate optimal disassembly sequences by considering the minimum number of directional changes as a fitness equation. In the proposed methodology, a stability graph is formulated for the considered assembly to apply cut-set rules for generating optimal assembly sequences. Later, the reverse of the obtained optimal assembly sequences is followed to generate the optimal disassembly sequences. In this strategy, along with the generation of optimal disassembly sequences, the type of disposal (like landfill, incineration and recycling) that has to follow for the individual parts is also discussed using a SOLIDWORKS sustainable tool. The proposed stability graph cut-set method is validated using an eleven-part punching machine assembly to generate the optimal disassembly sequences; also the type of disposal that has to follow for each part after dismantle is discussed. Moreover, the proposed methodology is compared to the well-known algorithms [genetic algorithm (GA) and ant colony optimization (ACO) algorithm] in terms of the number of iterations, the number of optimal disassembly sequences generated and fitness value to check the performance of the algorithm. © 2021, Indian Academy of Sciences.