In order to study the mechanical properties and damage evolution law of concrete with different zeolite powder (ZP) contents, natural aggregate concrete (ZPC) and recycled aggregate concrete (ZPRC) were prepared by replacing part of cement (C) with ZP, and uniaxial compression tests were carried out. The microstructure of the sample was characterized by nuclear magnetic resonance, scanning electron microscopy, energy dispersive X-ray spectroscopy, and acoustic emission (AE). The meso-damage evolution mechanism of ZPC and ZPRC was studied by using statistical damage theory. The results showed that when the replacement rate (R) of zeolite powder increased from 0% to 25%, the peak stress and elastic modulus of ZPC and ZPRC decreased by 39.31%, 29.93%, 56.17%, and 58.10%, respectively. The peak strain increased by 1.62 times and 2.44 times, respectively. When R is the same, ZPRC exhibits lower compressive strength and better deformation ability compared to ZPC. At the age of 28 days, ZP not only participated in the hydration reaction, but also increased the internal cracks and pores of the test block, deteriorating the internal structure of the concrete, and the deterioration effect played a dominant role. Compared to ZPC, ZPRC has a larger porosity. Based on the microscopic statistical damage theory, the relationship between five characteristic parameters and the replacement rate R was analyzed, and the influence of R on the evolution process of microscopic fracture and yield damage was discussed. An explanation was given for the phenomenon of the peak state of the acoustic emission test ringing count lagging behind the nominal stress-strain curve. The phenomenon that the peak state of AE test ringing count lags behind the nominal stress-strain curve is explained. The relationship between the macroscopic mechanical behavior of concrete and the microscopic damage mechanism has been established.