Methods for decontaminating toxic waste, particularly solid carrier materials, such as soil contaminated with a toxin, or solid mixed wastes are more efficiently decontaminated with solvated electrons by first extracting the toxin from the carrier with a nitrogenous base at elevated temperatures, followed by a temperature reduction before initiating chemical reduction of the toxin with solvated electrons. Pre-extraction of the toxin at elevated temperatures followed by temperature reduction minimizes competing side reactions, improves selectivity of solvated electrons for the toxin and improves the economics of the process with more efficient metal utilization. The process can be performed without separation of the toxin from the extraction vessel holding the solid carrier material. Alternatively, elevated temperatures can be used to perform one or more extractions of toxin with nitrogenous base followed by reduction with solvated electrons by performing the reaction in a separate reactor. The processes of the invention are useful in the destruction of virtually any chemically reducible hazardous substance.