Manganese can be an optimal alloying addition in lead-free SAC (SnAgCu) solder alloys because of its low price and harmless nature. In this research, the mechanical properties of the novel SAC0307 (Sn/Ag0.3/Cu0.7) alloyed with 0.7 wt.% Mn (designated as SAC0307-Mn07) and those of the traditionally used SAC305 (Sn96.5/Ag3/Cu0.5) solder alloys were investigated by analyzing the shear force and Vickers hardness of reflowed solder balls. During the preparation of the reflowed solder balls, different cooling rates were used in the range from 2.7 K/s to 14.7 K/s. After measuring the shear force and the Vickers hardness, the structures of the fracture surfaces and the intermetallic layer were investigated by SEM (Scanning Electron Microscopy). The mechanical property measurements showed lower shear force for the SAC0307-Mn07 alloy (20–25 N) compared with the SAC305 alloy (27–35 N), independent of the cooling rate. However, the SAC0307-Mn07 alloy was softer; its Vickers hardness was between 12 and 13 HV, whereas the Vickers hardness of the SAC305 alloy was between 19 and 20 HV. In addition, structural analyses revealed rougher intermetallic compound layers in the case of the SAC0307-Mn07 alloy, which can inhibit the propagation of cracks at the solder–substrate interface. These two properties of SAC0307-Mn07 alloy, the softer nature and the rougher intermetallic layer, might result in better thermomechanical behavior of the solder joints during the lifetime of electronic devices.