Spruce (Piceaabies) wood hemicelluloses have been obtained by the noncatalytic and catalytic oxidative delignification in the acetic acid-water-hydrogen peroxide medium in a processing time of 3–4 h and temperatures of 90–100 °C. In the catalytic process, the H2SO4, MnSO4, TiO2, and (NH4)6Mo7O24 catalysts have been used. A polysaccharide yield of up to 11.7 wt% has been found. The hemicellulose composition and structure have been studied by a complex of physicochemical methods, including gas and gel permeation chromatography, Fourier-transform infrared spectroscopy, and thermogravimetric analysis. The galactose:mannose:glucose:arabinose:xylose monomeric units in a ratio of 5:3:2:1:1 have been identified in the hemicelluloses by gas chromatography. Using gel permeation chromatography, the weight average molar mass Mw of hemicelluloses has been found to attain 47,654 g/mol in noncatalytic delignification and up to 42,793 g/mol in catalytic delignification. Based on the same technique, a method for determining the α and k parameters of the Mark–Kuhn–Houwink equation for hemicelluloses has been developed; it has been established that these parameters change between 0.33–1.01 and 1.57–472.17, respectively, depending on the catalyst concentration and process temperature and time. Moreover, the FTIR spectra of the hemicellulose samples contain all the bands characteristic of heteropolysaccharides, specifically, 1069 cm−1 (C–O–C and C–O–H), 1738 cm−1 (ester C=O), 1375 cm−1 (–C–CH3), 1243 cm−1 (–C–O–), etc. It has been determined by the thermogravimetric analysis that the hemicelluloses isolated from spruce wood are resistant to heating to temperatures of up to ~100 °C and, upon further heating, start destructing at an increasing rate. The antioxidant activity of the hemicelluloses has been examined using the compounds simulating the 2,2-diphenyl-2-picrylhydrazyl free radicals.