The development of new dual-functional materials for detection and removal of heavy metal ions is of great significance in environmental protection. Herein, a new amine-functionalized β-ketoenamine-linked covalent organic framework (termed as NH2–Th-Tfp COF) containing rich O,N,O′-chelating sites and free amine groups has been synthesized through the site-selective synthesis strategy under solvothermal conditions. The as-synthesized NH2–Th-Tfp COF shows strong fluorescence in water dispersion and can be used as highly sensitive and selective fluorescent probe for Cu2+ detection. As a sensing platform, the limit of detection for NH2–Th-Tfp COF toward Cu2+ ion is estimated to be 0.19 μM. Besides, the NH2–Th-Tfp COF possesses high adsorption capacity of 153 mg/g toward Cu2+ ion in aqueous solution. More importantly, this NH2–Th-Tfp COF exhibits higher sensitivity and larger adsorption capacity toward Cu2+ ion in comparison with the non-amine functionalized Th-Tfp COF, which may be attributed to the large number of free amine groups in the pore walls of NH2–Th-Tfp COF. The coordination interactions between Cu2+ ion with the O, N, O′-chelating sites and free amine groups in the pore walls of NH2–Th-Tfp COF can greatly enhance its recognition and absorption performances toward Cu2+ ion, as verified by X-ray photoelectron spectroscopy. This work may pave the way for designing new fluorescent COF materials with dual functions for simultaneous detection and removal of specific metal ions.