The rise of generative neural networks has triggered an increased demand for intellectual property (IP) protection in generated content. Deep watermarking techniques, recognized for their flexibility in IP protection, have garnered significant attention. However, the surge in adversarial transferable attacks poses unprecedented challenges to the security of deep watermarking techniques-an area currently lacking systematic investigation. This study fills this gap by introducing two effective transferable attackers to assess the vulnerability of deep watermarks against erasure and tampering risks. Specifically, we initially define the concept of local sample density, utilizing it to deduce theorems on the consistency of model outputs. Upon discovering that perturbing samples towards high sample density regions (HSDR) of the target class enhances targeted adversarial transferability, we propose the Easy Sample Selection (ESS) mechanism and the Easy Sample Matching Attack (ESMA) method. Additionally, we propose the Bottleneck Enhanced Mixup (BEM) that integrates information bottleneck theory to reduce the generator's dependence on irrelevant noise. Experiments show a significant enhancement in the success rate of targeted transfer attacks for both ESMA and BEM-ESMA methods. We further conduct a comprehensive evaluation using ESMA and BEM-ESMA as measurements, considering model architecture and watermark encoding length, and achieve some impressive findings.