In the market economy, mechanical engineering enterprises require continuous improvement of business processes to ensure their competitiveness and sustainable development. Improving business processes based on lean manufacturing and management accounting allows for gaining competitive advantages in the value-creating flow for the consumer and increasing the economic efficiency of the enterprise’s operations. This study takes into account the need to improve the management of material resources being cut at mechanical engineering enterprises with single and serial production types. The main direction for improving the cutting process of industrial materials is to increase their utilisation rate through the use of rational cutting methods. However, this study identifies unresolved problems in theory and practice related to managing business and non-business material resources obtained after cutting, which affect the elimination of material and time losses arising in the process of cutting. Among the main study results are advanced terminological apparatus in the field of cutting industrial materials, advanced techniques for sorting material resources obtained after cutting and methodological provisions for their valuation, methodological approach to assessing economic efficiency of the sorting decision, and software package prototype with elements of the decision-making support system for sorting materials obtained after cutting. The implications of these results are discussed, and directions for future research are suggested.