A dual-wavelength self-mode-locked monolithic Nd:YAG laser at 1061 and 1064 nm is realized at cryogenic temperatures. At an incident pump power of 5.5 W, the total output power can reach 2.5 W and the mode-locked pulse width is 29 ps at a pulse repetition rate of 7.75 GHz. The synchronization of the dual-wavelength emissions leads to a beat frequency of 670 GHz in the individual mode-locked pulse. It is further discovered that the laser output consists of two orthogonally polarized components with a central frequency difference of 127 MHz. The central frequency difference between two orthogonal polarizations mainly arises from the external mechanical stress introduced by the copper holder for the laser crystal.