Lignocellulosic biomass represents one of the most important feedstocks for future biorefineries, being a precursor of valuable bio-products, obtainable through both chemical and biological conversion routes. Lignocellulosic biomass has a complex matrix, which requires the careful development of multi-step approaches for its complete exploitation to value-added compounds. Based on this perspective, the present work focuses on the valorization of hemicellulose and cellulose fractionsof giant reed (Arundo donax L.) to give second-generation sugars, minimizing the formation of reaction by-products. The conversion of hemicellulose to xylose was undertaken in the presence of the heterogeneous acid catalyst Amberlyst-70 under microwave irradiation. The effect of the main reaction parameters, such as temperature, reaction time, catalyst, and biomass loadings on sugars yield was studied, developing a high gravity approach. Under the optimised reaction conditions (17 wt% Arundo donax L. loading, 160 °C, Amberlyst-70/Arundo donax L. weight ratio 0.2 wt/wt), the xylose yield was 96.3 mol%. In the second step, the cellulose-rich solid residue was exploited through the chemical or enzymatic route, obtaining glucose yields of 32.5 and 56.2 mol%, respectively. This work proves the efficiency of this innovative combination of chemical and biological catalytic approaches, for the selective conversion of hemicellulose and cellulose fractions of Arundo donax L. to versatile platform products.