Using a biorefinery approach, biomass polymers such as lignin and carbohydrates can be selectively purified from lignocellulosic feedstocks with the aim of generating not only lignocellulosic bioethanol but also high value bio-based compounds. Furthermore, the efficient use of the entire biomass can increase overall feedstock value and significantly contribute to process cost-effectiveness. Therefore, the aim of this work was to fractionate the main compounds of the energy crop Miscanthus x giganteus (MxG) using 'green' solvents in order to obtain cellulose-enriched fibres as well as non-toxic streams rich in hemicellulose and lignin. Two processing routes were compared: a direct 1-step modified organosolv method for simultaneous lignin and hemicellulose removal; and a 3-step sequential process using subcritical water extraction for recovery of first extractives then hemicellulose, followed by modified organosolv lignin extraction. Both methods successfully generated cellulose-enriched fibres; from a complex mixture of compounds present in MxG, it was possible to obtain fibres comprising 78% cellulose without the use of commonly-applied toxic solvents that can potentially limit end uses for processed biomass and/or need additional neutralization steps. Fibres generated by the direct and sequential processes were very similar in composition; however, physicochemical analysis of the fibres using scanning electron microscopy, Fourier-transform infrared spectroscopy and principal component analysis confirmed structural differences resulting from the two processing routes, which were demonstrated to have an impact on downstream processing.