Coal mining often causes periodic disruption in the rock mass around the stope. The study of the deformation and failure characteristics of cyclic loading and unloading sandstone is very critical for gaining a thorough understanding of the mechanisms of rock damage, degradation, and failure. This kind of investigation is very helpful in determining the precursors of rock failure and the instability of engineering structures. In this research study, the properties of acoustic emission and infrared radiation of cyclic loading and unloading sandstone are explored using a cyclic loading and unloading sandstone experiment. Based on acoustic emission and infrared radiation, the loading–unloading response ratio of rock is established. It is found that the response variables of sandstone during the loading stage based on acoustic emission (AE) counts and the loading–unloading response ratio based on average infrared radiation temperature (AIRT) both rise suddenly in the last cycle, which may be a precursor of “acoustic-thermal” approaching rock failure. On this basis, the quantitative analysis index of infrared radiation of differential infrared energy change rate (DIECR) is proposed, that is, the change of square of ΔAIRT in unit time, and based on AE counts and DIECR, the loading–unloading response ratio of “acoustic-thermal” is defined. It is found that the “acoustic-thermal” loading–unloading response ratio suddenly increases during the penultimate cycle of loading and unloading. This feature can be taken as the initial precursor of rock failure. Together with the “acoustic-thermal” imminent failure precursor of rock, it constitutes the “initial precursor-imminent failure precursor” combined with the internal fracture and surface infrared radiation temperature field during the cyclic loading and unloading process of rock, realizing the hierarchical monitoring and early warning of cyclic loading and unloading rock failure. The research results lay a theoretical and practical foundation for using infrared radiation to monitor engineering disasters caused by rock fracture and failure in mining engineering.