The degradation of the complex structure of lignocellulosic biomass is important for its further biorefinery to value-added bioproducts. The use of effective fungal species for the optimised degradation of biomass can promote the effectiveness of the biorefinery of such raw material. In this study, the optimisation of processing parameters (temperature, time, and s/w ratio) for cellulase activity and reducing sugar (RS) production through the hydrolysis of sugar beet pulp (SBP) by edible filamentous fungi of Aspergillus, Fusarium, Botrytis, Penicillium, Rhizopus, and Verticillium spp. was performed. The production of RS was analysed at various solid/water (s/w) ratios (1:10–1:20), different incubation temperatures (20–35 °C), and processing times (60–168 h). The Aspergillus niger CCF 3264 and Penicillium oxalicum CCF 3438 strains showed the most effective carboxymethyl cellulose (CMC) degrading activity and also sugar recovery (15.9–44.8%) from SBP biomass in the one-factor experiments. Mathematical data evaluation indicated that the highest RS concentration (39.15 g/100 g d.w.) and cellulolytic activity (6.67 U/g d.w.) could be achieved using A. niger CCF 3264 for the degradation of SBP at 26 °C temperature with 136 h of processing time and a 1:15 solid/water ratio. This study demonstrates the potential of fungal degradation to be used for SBP biorefining.