The stress-strain curves under cyclic compressive loading are essential for analyzing the performance of structures subjected to dynamic actions, such as wind, and earthquake. This study adopted cyclic compressive tests to obtain the stress-strain curves of seawater and sea sand concrete (SSC). Meanwhile, the mechanical properties of SSC were also investigated under monotonic compressive loading for a better comparison. The influence of the fly ash content on the properties of SSC was explored as well. The test results show that without the addition of fly ash, SSC and the concrete mixed with tap water and desalted sea sand shared similar compressive strength and modulus. As the amount of fly ash increased from 0 to 60% of the cement by weight, the compressive strength and modulus of SSC showed a fluctuating trend. With the consideration of both mechanical properties and carbon emissions, replacing 40% cement with fly ash in SSC seemed to be a good choice. At the same amount of fly ash, the compressive strength of SSC under cyclic loading was slightly smaller than that under monotonic loading. According to the experimental curves, theoretical models were established to capture the characteristics of the stress-strain curves under both monotonic and cyclic compressive loading. The models were in good agreement with the experimental ones. Meanwhile, the unloading characteristics of the curves were also captured and modeled. Moreover, the damage factor values of SSC were identified and can be adopted for the model of concrete damaged plasticity, which can be incorporated into finite element methods. The results from this paper contribute to the understanding of the behavior of SSC under both monotonic and cyclic compressive loading, and provide proper stress-strain models for assessing the structural performance.