Copper slag (CS), an industrial by-product, can be used as supplementary cementitious materials in the mortar to achieve sustainable development of the copper and the cement industries. However, available evaluation and prediction models for CS cementitious material considering the comprehensive effect of multiple factors are very scarce. In this study, a reliable experimental database with 141 sets of data was developed via compressive strength tests and reviews of the literature at first. Subsequently, the gray correlation analysis was performed to evaluate the correlation between the influencing factors and the compressive strength of mortar with CS addition. The results demonstrated that the strength was most sensitive to the water to binder ratio and CS chemical composition, which could not be ignored to compare and evaluate the strength acquired from different works. Besides, for the same batch CS used in this study, the compressive strength at 3 d depended on the curing program; while it was more easily affected by the CS fineness after 28 d. Finally, a reliable prediction model for the compressive strength of the mortar with CS addition was implemented by the back-propagation neural network. The established network with four neurons in the hidden layer had a high accuracy as well as a good generalization ability, which can be used as an effective tool for detecting trends of the compressive strength and designing CS-added mortar with a user-defined compressive strength.