With the increasing release of powerful language models trained on large code corpus (e.g. CodeBERT was trained on 6.4 million programs), a new family of mutation testing tools has arisen with the promise to generate more "natural" mutants in the sense that the mutated code aims at following the implicit rules and coding conventions typically produced by programmers. In this paper, we study to what extent the mutants produced by language models can semantically mimic the observable behavior of security-related vulnerabilities (a.k.a. Vulnerability-mimicking Mutants), so that designing test cases that are failed by these mutants will help in tackling mimicked vulnerabilities. Since analyzing and running mutants is computationally expensive, it is important to prioritize those mutants that are more likely to be vulnerability mimicking prior to any analysis or test execution. Taking this into account, we introduce VMMS, a machine learning based approach that automatically extracts the features from mutants and predicts the ones that mimic vulnerabilities. We conducted our experiments on a dataset of 45 vulnerabilities and found that 16.6% of the mutants fail one or more tests that are failed by 88.9% of the respective vulnerabilities. More precisely, 3.9% of the mutants from the entire mutant set are vulnerability-mimicking mutants that mimic 55.6% of the vulnerabilities. Despite the scarcity, VMMS predicts vulnerability-mimicking mutants with 0.63 MCC, 0.80 Precision, and 0.51 Recall, demonstrating that the features of vulnerability-mimicking mutants can be automatically learned by machine learning models to statically predict these without the need of investing effort in defining such features.