Sound Event Detection (SED) systems are increasingly deployed in safety-critical applications such as industrial monitoring and audio surveillance. However, their robustness against adversarial attacks has not been well explored. Existing audio adversarial attacks targeting SED systems, which incorporate both detection and localization capabilities, often lack effectiveness due to SED's strong contextual dependencies or lack precision by focusing solely on misclassifying the target region as the target event, inadvertently affecting non-target regions. To address these challenges, we propose the Mirage and Mute Attack (M2A) framework, which is designed for targeted adversarial attacks on polyphonic SED systems. In our optimization process, we impose specific constraints on the non-target output, which we refer to as preservation loss, ensuring that our attack does not alter the model outputs for non-target region, thus achieving precise attacks. Furthermore, we introduce a novel evaluation metric Editing Precison (EP) that balances effectiveness and precision, enabling our method to simultaneously enhance both. Comprehensive experiments show that M2A achieves 94.56% and 99.11% EP on two state-of-the-art SED models, demonstrating that the framework is sufficiently effective while significantly enhancing attack precision.