To contribute to the development of sustainable composites, this work investigates the effects of moisture on the key AE characteristics related to the damage mechanisms of a bio-based balsa wood core sandwich in 4-point bending tests, including cumulative counts, amplitude, peak frequency, and duration. Novel triple dog-bone balsa wood core sandwich specimens with different MC (moisture content) were studied by comparing microscopic observations and a proposed two-step clustering approach in AE analysis. Three MC states, i.e., dry, 50% MC, and 120% MC, are discussed. GFRP (glass-fiber-reinforced polymer) laminate skin damages were found to be predominant in most GFRP–balsa sandwich specimens, but balsa wood core damages play a more important role as MC increases. The degradation of the bending stiffness of the sandwich was proven to be faster in the first linear stage of the moisture absorption curve, while the decrease in bending strength was more pronounced at the MC saturation level. Finally, for all of the dry and wet sandwich specimens, peak frequency and duration were proven to be more helpful in identifying damages associated with the lighter bio-based balsa wood core, such as balsa core damages and skin/core debonding.