The effect of inorganic binder-based extrusion (Silica sol, Bentonite, Attapulgite, and SB1) in the selective adsorption of CO2, CH4, and N2 on zeolite 13X in the context of flue gas carbon capture and natural gas purification has been studied to reduce CO2 emissions. The effect of extrusion with binders was examined by adding 20 wt% of the mentioned binders to pristine zeolite and the results were analyzed by four approaches; (i) the effect on structural properties was analyzed by XRD patterns followed by Williamson–Hall (W–H) plot, FESEM images, and BET surface area. In addition, the mechanical strength of the shaped zeolites was measured by crush resistance testing; (ii) the effect on the adsorption capacity for CO2, CH4, and N2 were measured by volumetric apparatus up to 100 kPa; (iii) the impact on binary separation (CO2/CH4 and CO2/N2) were investigated; (iv) the influence on diffusion coefficients were estimated by micropore and macropore kinetic model. The results showed that the presence of a binder can cause reductions in BET surface area and pore volume, indicating partial pore blockage. It was found that the Sips model had the best adaptability to the experimental isotherms data. The trend of CO2 adsorption was 13X > pseudo-boehmite > bentonite > attapulgite > silica, in which the adsorption capacity reached 6.02, 5.60, 5.24, 5.00, and 4.71 mmol/g, respectively. Among all samples, silica was found the most suitable binder for CO2 capture in terms of selectivity, mechanical stability, and diffusion coefficients.