The mechanical properties of solder alloys are a performance that cannot be ignored in the field of electronic packaging. In the present study, novel Sn-Zn solder alloys were designed by the cluster-plus-glue-atom (CPGA) model. The effect of copper (Cu) addition on the microstructure, tensile properties, wettability, interfacial characterization and melting behavior of the Sn-Zn-Cu solder alloys were investigated. The Sn29Zn4.6Cu0.4 solder alloy exhibited a fine microstructure, but the excessive substitution of the Cu atoms in the CPGA model resulted in extremely coarse intermetallic compound (IMC). The tensile tests revealed that with the increase in Cu content, the tensile strength of the solder alloy first increased and then slightly decreased, while its elongation increased slightly first and then decreased slightly. The tensile strength of the Sn29Zn4.6Cu0.4 solder alloy reached 95.3 MPa, which was 57% higher than the plain Sn-Zn solder alloy, which is attributed to the fine microstructure and second phase strengthening. The spreadability property analysis indicated that the wettability of the Sn-Zn-Cu solder alloys firstly increased and then decreased with the increase in Cu content. The spreading area of the Sn29Zn0.6Cu0.4 solder alloy was increased by 27.8% compared to that of the plain Sn-Zn solder due to Cu consuming excessive free state Zn. With the increase in Cu content, the thickness of the IMC layer decreased owing to Cu diminishing the diffusion force of Zn element to the interface.