Designing bio-based adhesives with multiple crosslinking networks has significant implications for the green and sustainable development of the forestry industry. A sawdust based crosslinking network adhesive system was constructed by a small molecule covalent bridge and a hydrogen bond grafting chain thioctic acid (TA) supramolecule with oxidized sawdust (OS) as the carrier with the covalent bond as the first network and the hydrogen bond as the second network, which realized the toughening and strengthening of the oxidized sawdust/thioctic acid (OSTA) adhesive. Furthermore, the wood interface was regulated by 3-glycidyl ether oxy propyl trimethoxysilane, which introduced active epoxy groups to the wood interface. Then, the third interfacial covalent network was constructed by the reaction of interfacial active groups with the carboxyl group, hydroxyl group, and amino group in the OSTA adhesive system. The dry bonding strength of the OSTA-modified adhesive can reach 2.09 MPa, which is 75.6% and 50.4% higher than that of the OS and TA adhesives, respectively, and the water resistance strength is increased from 0 MPa of OS and 1.25 MPa of TA to 1.71 MPa. In addition, the OSTA adhesive not only shows adhesion performance for wood but also manifests excellently on various surface energy substrates, such as skin, glass, ceramics, plants, rubber, stainless steel, etc., with multi-functional adhesion properties. This work broadens the prospects of OSTA adhesive applications in various scenarios.