Functionalized two-dimensional Ti3C2Tx (TN-EHL) was prepared as an effective adsorbent for removal of methylene blue dye (MB) and copper ions (Cu2+). Enzymatic hydrolysis lignin (EHL), a reproducible natural resource, was used to functionalize the Ti3C2Tx nanosheets. EHL can not only introduce active functional groups into TN-EHL but also prevent the oxidation of Ti3C2Tx, thus promoting the adsorption performance of TN-EHL. The maximum adsorption capacities of TN-EHL50 (in which the EHL content is 50 wt%) for MB and Cu2+ were 293.7 mg g−1 and 49.96 mg g−1, respectively. The higher correlation coefficients (R2) of MB (0.9996) and Cu2+ (0.9995) indicating that their adsorption processes can be described by the pseudo-second-order kinetic model. The MB adsorption data fit the Freundlich isotherm with R2 of 0.9953, whereas the Cu2+ ions adsorption data fit the Langmuir isotherm with R2 of 0.9998. The thermodynamic analysis indicates that the adsorption process of MB and Cu2+ on TN-EHL50 is spontaneous and endothermic. Significantly, the Cu2+ ions were reduced to Cu2O and CuO particles during the adsorption process. Therefore, TN-EHL has a great potential as an environmentally friendly adsorbent for MB removal and recovery of Cu2+ ions from wastewater.