Survival analysis (SA) models have been widely studied in mining electronic health records (EHRs), particularly in forecasting the risk of critical conditions for prioritizing high-risk patients. However, their vulnerability to adversarial attacks is much less explored in the literature. Developing black-box perturbation algorithms and evaluating their impact on state-of-the-art survival models brings two benefits to medical applications. First, it can effectively evaluate the robustness of models in pre-deployment testing. Also, exploring how subtle perturbations would result in significantly different outcomes can provide counterfactual insights into the clinical interpretation of model prediction. In this work, we introduce SurvAttack, a novel black-box adversarial attack framework leveraging subtle clinically compatible, and semantically consistent perturbations on longitudinal EHRs to degrade survival models' predictive performance. We specifically develop a greedy algorithm to manipulate medical codes with various adversarial actions throughout a patient's medical history. Then, these adversarial actions are prioritized using a composite scoring strategy based on multi-aspect perturbation quality, including saliency, perturbation stealthiness, and clinical meaningfulness. The proposed adversarial EHR perturbation algorithm is then used in an efficient SA-specific strategy to attack a survival model when estimating the temporal ranking of survival urgency for patients. To demonstrate the significance of our work, we conduct extensive experiments, including baseline comparisons, explainability analysis, and case studies. The experimental results affirm our research's effectiveness in illustrating the vulnerabilities of patient survival models, model interpretation, and ultimately contributing to healthcare quality.