Assembly of naturally occurring building blocks into functional materials is of great importance. Herein, we utilized plant-derived polyphenols as building blocks to prepare porous organic polymers (POPs) with multifunctional sites, and a typical POP (denoted as GA-azo-POP) could be achieved from gallic acid through an azo-coupling strategy. As a superior support, GA-azo-POP supported Ag nanoparticles could efficiently catalyze the carboxylative cyclization of propargyl alcohols with CO2 with a very low usage of Ag (0.14 mol%). Meanwhile, the GA-azo-POP showed a high capacity for I2 adsorption (up to 287 mg g−1), which was higher than that of the reported solid materials at a similar I2 concentration. More interestingly, after adsorbing I2, the GA-azo-POP could efficiently catalyze the formation of cyclic carbonates from CO2. The excellent performance of the GA-azo-POP resulted from the co-existence of aromatic, azo, and phenolic OH functional groups and its porous structure.