High-power single-longitudinal-mode (SLM) lasers are crucial for applications such as LIGO, sodium guide stars, isotope separation and atom cooling, but are challenging due to gain profile inhomogeneities and spatial hole burning. This work shows that a SLM 620 nm laser is firstly achieved using a standing-wave diamond Raman resonator with intracavity second harmonic generation (SHG). In addition to the benefits of the spatial hole burning-free gain medium , SHG provides a valuable additional mechanism for increasing gain competition and therefore enhancing SLM stability. Nascent secondary modes experience double the nonlinear loss in the SHG crystal due to the role of sum frequency generation with the primary mode . A further feature of the current external standing-wave cavity design is that the cavity is non-resonant at the pump frequency, thereby allowing the laser to be pumped without mutual control of the wavelength and cavity length and by using multi-longitudinal-mode (MLM) lasers with a spacing different to the free-spectral-range of the diamond Raman laser.