Embedding-as-a-Service (EaaS) has emerged as a successful business pattern but faces significant challenges related to various forms of copyright infringement, including API misuse and different attacks. Various studies have proposed backdoor-based watermarking schemes to protect the copyright of EaaS services. In this paper, we reveal that previous watermarking schemes possess semantic-independent characteristics and propose the Semantic Perturbation Attack (SPA). Our theoretical and experimental analyses demonstrate that this semantic-independent nature makes current watermarking schemes vulnerable to adaptive attacks that exploit semantic perturbations test to bypass watermark verification. To address this vulnerability, we propose the Semantic Aware Watermarking (SAW) scheme, a robust defense mechanism designed to resist SPA, by injecting a watermark that adapts to the text semantics. Extensive experimental results across multiple datasets demonstrate that the True Positive Rate (TPR) for detecting watermarked samples under SPA can reach up to more than 95%, rendering previous watermarks ineffective. Meanwhile, our watermarking scheme can resist such attack while ensuring the watermark verification capability. Our code is available at this https URL.