Drought stress severely limits peanut productivity, highlighting the urgent need to understand the molecular mechanisms that underlie drought adaptation. While microRNAs (miRNAs) are known to play essential roles in plant stress responses, their functional contributions in polyploid crops like peanut remain insufficiently explored. This study provides the first integrated transcriptomic analysis of drought-responsive miRNAs in tetraploid peanut (Arachis hypogaea). We performed high-throughput sRNA sequencing on a drought-tolerant cultivar Fenhua 8 under PEG6000-simulated drought stress, identifying 10 conserved drought-responsive miRNAs. Among these, ahy-miR398 and ahy-miR408 were significantly downregulated under drought conditions. Degradome sequencing revealed that ahy-miR398 targets copper chaperones for superoxide dismutase (CCSs), potentially reducing SOD activation and amplifying oxidative stress. In contrast, ahy-miR408 targets laccase 12 (LAC12), P-type ATPase copper transporters (COPAs), and a blue copper protein-like (PCL) gene. These targets are involved in copper homeostasis and the regulation of reactive oxygen species (ROS), suggesting that ahy-miR408 plays a role in oxidative stress management. Functional validation in transgenic Arabidopsis lines overexpressing ahy-miR398 or ahy-miR408 showed significantly reduced drought tolerance, with impaired seed germination, shorter primary roots, and exacerbated growth suppression during water deprivation. Taken together, these findings highlight a novel miRNA-mediated regulatory network in peanut drought adaptation, centered on copper-associated oxidative stress management. This study provides new insights into miRNA-based regulation in polyploid crops and offers potential molecular targets for breeding climate-resilient peanut varieties, especially in arid regions where yield stability is crucial.