To investigate the relationships between the different mechanical strengths of internally cured concrete with Super Absorbent Polymer (SAP concrete), the uniaxial mechanical properties of SAP concrete with different internal curing water-cement ratios were studied. Various SAP concrete specimens were prepared, and the uniaxial compressive, splitting tensile, as well as four-point bending tests, were carried out using the electro-hydraulic servo testing machine. The cubic compressive strength, splitting tensile strength, and flexural strength of SAP concrete with different internal curing water-cement ratios was obtained. The converting relationships between the internal curing water-cement ratio and different mechanical strengths were analyzed extensively. Based on the conversion formulas of different strength indexes proposed by different national standards and other researchers, the equations among the splitting tensile strength, cubic compressive strength, and flexural strength of SAP concrete were proposed and verified using the experimental data. According to the comparative analysis results, the proposed equations in this study have significant applicability and can be conducted in the practical application of SAP concrete.