Phenolic compounds are one of the main organic pollutants in the environment that can seriously affect ecosystems, even at very low concentrations. Due to the resistance of phenolic compounds to microorganisms, conventional biological treatment methods face challenges in effectively addressing this pollution problem. In this study, a novel laccase mimic (Tris-Cu nanozyme) is prepared using a simple and rapid synthesis strategy based on the coordination of copper ions and amino groups in Tris(hydroxymethyl)aminomethane (Tris). It is found that the Tris-Cu nanozyme exhibits good catalytic activity against a variety of phenolic compounds, the Km, Vmax and Kcat are determined to be 0.18 mM, 15.62 μM·min−1 and 1.57 × 107 min−1 using 2,4-dichlorophenol (2,4-DP) as the substrate, respectively. Then, based on the laccase-like activity of the Tris-Cu nanozyme, a novel colorimetric method for 2,4-DP (the limit of detection (LOD) = 2.4 μM, S/N = 3) detection in the range of 10–400 μM was established, and its accuracy was verified by analyzing tap and lake water samples. In addition, the Tris-Cu nanozyme shows excellent removal abilities for six phenolic compounds in experiments. The removal percentages for 2,4-DP, 2-chlorophenol (2-CP), phenol, resorcinol, 2,6-dimethoxyphenol (2,6-DOP), and bisphenol A (BPA) are 100%, 100%, 100%, 100%, 87%, and 81% at 1 h, respectively. In the simulated effluent, the Tris-Cu nanozyme maintains its efficient catalytic activity towards 2,4-DP, with a degradation percentage of 76.36% at 7 min and a reaction rate constant (k0) of 0.2304 min−1. Therefore, this metal–organic complex shows promise for applications in the monitoring and degrading of environmental pollutants.