Lignocellulosic biomass including agricultural residues and by-products, and woody biomass are produced worldwide in large amounts every year. With the exception of limited-usage areas, these materials are regarded as waste. Therefore, renewable lignocellulosic biomass is gaining considerable attention because of its potential for use in the production of biofuels and other value-added products. In this study, the co-production of two value-added products, xylanase (enzyme) and xylooligosaccharides (XO), was investigated by utilizing lignocellulosic biomass residues within a multi-product biorefinery framework. Box–Behnken design-based response surface methodology was employed to optimize culture parameters for xylanase production from a thermophilic fungus, Scytalidium thermophilum, and the enzyme was biochemically characterized. Optimized media conditions resulted in an approximately 2-fold increase in xylanase activity compared to the initial conditions. Crude enzyme solution was capable of producing XO from the hemicellulosic fraction of various biomass residues. The highest hemicellulose extraction yield was achieved from corn cob (37.7 ± 1.5%), followed by wheat bran (26.6 ± 0.8%) and cotton stalks (22.2 ± 0.6%). The highest reducing end concentration was obtained from sunflower seed shell (4.89 ± 0.02 mg mL−1), followed by sunflower stalks (4.41 ± 0.03 mg mL−1) and corn cob (3.49 ± 0.09 mg mL−1). Accordingly, corn cob yielded the highest XO production (172.1 mg XO per g raw biomass residue) with the main products of xylose (X1) and xylobiose (X2). In terms of the hemicellulosic fraction, beechwood had the maximum XO yield with 793 mg XO per g hemicellulose. Sunflower seed shell hydrolysis yielded mainly X1 and xylotetrose (X4) without X2 and xylotriose (X3). After 1 h of reaction time, X2 and higher sugars were obtained from the commercial beechwood xylan, while only X1 and X4 were obtained after 6 h. Xylose-free xylobiose was obtained from sugar beet bagasse and wheat bran, which are regarded as potential XO sources because XO with degrees of polymerization from 2–4 are preferred in food applications and XO without xylose are important in the food industry from a prebiotic point of view.