Ni-based single crystal (SX) superalloy with low specific weight is vital for developing aero engines with a high strength-to-weight ratio. Based on an alloy system with 3 wt.% Re but without W, namely Ni-Co-Cr-Mo-Ta-Re-Al-Ti, a specific weight below 8.4 g/cm³ has been achieved. To reveal the relationship among the composition, mechanical properties, and thermal stability of Ni-based SX superalloys, SXs with desirable microstructures are fabricated. Tensile tests revealed that the SX alloys have comparable strength to commercial second-generation SX CMSX-4 (3 wt.% Re and 6 wt.% W) and Rene′ N5 alloys (3 wt.% Re and 5 wt.% W) above 800 °C. Moreover, the elongation to fracture (EF) below 850 °C (>20%) is better than that of those two commercial SX superalloys. During thermal exposure at 1050 °C for up to 500 h, the topological close-packed (TCP) phase does not appear, indicating excellent phase stability. Decreasing Al concentration increases the resistance of γ′ rafting and replacing 1 wt.% Ti with 3 wt.% Ta is beneficial to the stability of the shape and size of γ′ phase during thermal exposure. The current work might provide scientific insights for developing Ni-based SX superalloys with low specific weight.