Traditional methods of waste tires disposal have the drawbacks of land occupation, air pollution, high recycling costs, and low efficiency. The application of rubber particle-sand mixtures (RSMs) made by mixing waste tire fragments with sand in civil engineering can effectively solve the above problems, but its long-term deformation response has rarely received attention. In this study, the compression characteristics of RSM with four rubber contents under varying loading levels were investigated through a series of long-term compression tests, and the deformation development patterns under single-stage and multistage loading conditions were compared. The results indicate that the compression deformation of RSM consists of immediate compression and time-dependent compression. The immediate compression increases with the increase of rubber content and vertical load, whereas the time-dependent compression is proportional to the rubber content, vertical load, and loading time. The rate of compression deformation is primarily influenced by the rubber content and vertical load, and the loading time-creep relationship predicted by the logarithmic model is in good agreement with the experimental results. The influence of loading paths is mainly reflected in the total compression, with specific differences depending on the duration of the single-stage loading. On this basis, the compression mechanism of RSM was explained. The research results can provide valuable insights for the practical engineering application of RSM.