Inspired by the wings of owls and the tubercles present on humpback whales' flippers, leading-edge serrations have demonstrated the potential to mitigate airfoil–turbulence interaction noise. To deepen our understanding of the underlying mechanisms driving this noise reduction, we conducted compressible large-eddy simulations on a rod-airfoil configuration equipped with wavy leading edges (WLEs) of varying amplitudes. All tested serrations exhibited some degree of noise reduction, with the amplitude of the WLE exerting a significant influence on the overall noise reduction effect. Notably, the wavy airfoil with the largest amplitude demonstrated the most substantial noise reduction in the mid-frequency range, achieving a remarkable decrease in up to 2.2 dB in noise levels. Applying multi-process acoustic theory, we delved into sound production on surfaces and near-field structures responsible for generating noise sources. Our findings underscore a crucial mechanism contributing to noise reduction—the source cutoff effects manifested through the significant weakening of noise sources at hill regions along the serrations' surface. Stronger source cutoff effects were observed with larger WLE amplitudes. Furthermore, our study reveals that destructive relationships among sources also play a pivotal role in reducing flow noise. The reduction in mid-frequency noise results from a synergy of the source cutoff effect and destructive source relationships induced by WLEs, while the decrease in low-frequency noise primarily emanates from the source cutoff effect.