The growing awareness of nature conservation encourages producers, engineers, and designers to contribute to the rational and innovative use of raw materials. Sustainable development is imperative, symbolizing the balance between meeting the needs of the present generations without compromising the needs of future ones. The aim of this paper is to investigate the production process of cut veneer of Pedunculate Slavonian oak (Quercus robur L.) and which parts of the logs are lost or thrown in the production of cut veneer, to analyze the increase in the use of veneers that currently represent residue in processing, and to propose directions of designing a new product from the analyzed residue—decorative wall panels. The research was conducted in the company Spačva Ltd. in Vinkovci, Vukovar-Srijem County, Croatia, in 2021/2022. The findings emphasize that the vast majority of unused veneers, considered technologically unacceptable in the production process, can be decoratively and visually desirable due to their natural appearance in the design of a new product. By analyzing and applying the design principles and elements, natural phenomena were applied to the veneers that represent the basic motif of the new decorative wall panels. The initial solutions of the decorative wall coverings made of veneer with a natural appearance and the solution from other wood residues from production are shown. The results of this study have potentially far-reaching implications for wood product manufacturers and demonstrate the importance of applying design in wood technology to reduce residue, demonstrating that residue from standard production can be designed into an innovative, sustainable product that reduces environmental damage.