The paper describes the process of obtaining geopolymer composites using raw materials from critical waste, i.e., mixed power plant ash and furnace slag powder. Using such geopolymer composites, structural insulation panels were made in the laboratory, which were subjected to tests specific to construction applications. At the same time, some special properties, such as sound insulation and electromagnetic shielding properties for special applications, were tested. The results obtained from the functional tests led to the conclusion that the panels made of geopolymer composites provided both sound and electromagnetic attenuation values clearly superior to those obtained from autoclaved cellular concrete, brick, or concrete structures, which encourages us to suggest such material concepts for complex shielding purposes. The sustainability of the technology for producing such geopolymer composites was fully demonstrated from the economic, environmental, and social perspectives.