As CO2 emissions increase and the global climate deteriorates, converting CO2 into valuable chemicals has become a topic of wide concern. The development of multifunctional catalysts for efficient CO2 conversion remains a major challenge. Herein, two porous organic polymers (NPOPs) functionalized with covalent triazine and triazole N-heterocycles are synthesized through the copper(I)-catalyzed azide–alkyne cycloaddition (CuAAC) reaction. The NPOPs have an abundant microporous content and high specific surface area, which confer them excellent CO2 affinities with a CO2 adsorption capacity of 84.0 mg g−1 and 63.7 mg g−1, respectively, at 273 K and 0.1 MPa. After wet impregnation and in situ reductions, Ag nanoparticles were supported in the NPOPs to obtain Ag@NPOPs with high dispersion and small particle size. The Ag@NPOPs were applied to high-value conversion reactions of CO2 with propargylic amines and terminal alkynes under mild reaction conditions. The carboxylative cyclization transformation of propargylic amine into 2-oxazolidinone and the carboxylation transformation of terminal alkynes into phenylpropiolic acid had the highest TOF values of 1125.1 and 90.9 h−1, respectively. The Ag@NPOP-1 was recycled and used five times without any significant decrease in catalytic activity, showing excellent catalytic stability and durability.