The granular material (GM) is able to effectively improve the membrane fouling control in membrane bioreactor (MBR) by dynamic scouring, adsorption behavior and enzymatic degradation. However, their roles and effects on the filtration performance of MBR remain unclear. The present work investigated the GM dynamic scouring mechanism, revealed the multifunctional quantitative evaluation, and clarified the filtration performance at various GM operating conditions in MBR. First, the aerobic granular sludge (AGS)-filtration process was still limited by the presence of irreversible membrane fouling, which decreased the filtration performance in MBR (threshold flux [169.5 L m−2 h−1] and (turning point of membrane fouling resistance [1.1 × 1012 m−1]). To solve this problem, the GMs (activated carbon [AC] and laccase immobilized activated carbon [LAC]) was added into the AGS-filtration process to enhance the filtration performance. Above all, based on momentum conservation, the dynamic scouring mathematical model was put forward to elucidate the dynamic scouring mechanism of GM towards the membrane surface. The scouring stress on the membrane surface was proportional to the total mass of GM and offered an additional shear effect for clearly promoting the collision between GM and foulant, and decreasing their deposition on the membrane surface via friction with the membrane. Then, both AC and LAC exhibited a highly desirable adsorption efficiency for foulant removal, whereas the enzymatic degradation of LAC also furtherly straightened this effect. Furthermore, a new contribution quantification model was proposed for evaluating the contribution rates of dynamic scouring (59.1%), adsorption behavior (36.4%) and enzymatic degradation (4.6%) to boost the filtration performance, implying that the dynamic scouring and adsorption behavior brought about the dominated promotion. At the GM of 8 g/L and size of 300–600 μm, AGS-filtration exhibited an optimized performance in term of threshold flux, turning point of membrane fouling resistance and membrane cleaning. The present study offers insights into the mechanism that GM multifunctional scouring enhanced filtration performance in MBR.