The present study is aimed to investigate the post-critical behavior of a side-box steel-concrete composite girder under varying wind angles of attack, by conducting a series of section model testing with single-degree and two-degrees of freedom. The essence of flutter, as well as the adverse impact of vortex shedding lock-in on exacerbating post-critical flutter responses, was revealed in detail. The results indicate that the coupled motion of flutter for the prototype composite girder can be characterized as a supercritical Hopf bifurcation with significant phase shifting between motions. The circular character of the limit cycle oscillation (LCO) expressed in the phase diagram is altered to a non-circular form due to the apparent aerodynamic stiffness nonlinearity within a wide range of wind speeds. Interestingly, the coupling vibration between vortex-induced vibrations (VIV) and flutter, i.e., VIV-flutter coupling vibration is observed for the prototype girder, due to the evolution of total damping ratio concave shape with wind speed. Two mitigation countermeasures, i.e., a L-shaped skirt plate and a sharpened wind fairing, were proposed to improve the aeroelastic stability, caused by a significant increase in uncoupled positive aerodynamic damping and alternation of VIV-flutter coupling. In addition, the specific effects of structural damping on the VIV-flutter coupling were discussed in detail.