Survival analysis is employed to analyze the time before the event of interest occurs, which is broadly applied in many fields. The existence of censored data with incomplete supervision information about survival outcomes is one key challenge in survival analysis tasks. Although some progress has been made on this issue recently, the present methods generally treat the instances as separate ones while ignoring their potential correlations, thus rendering unsatisfactory performance. In this study, we propose a novel Deep Survival Analysis model with latent Clustering and Contrastive learning (DSACC). Specifically, we jointly optimize representation learning, latent clustering and survival prediction in a unified framework. In this way, the clusters distribution structure in latent representation space is revealed, and meanwhile the structure of the clusters is well incorporated to improve the ability of survival prediction. Besides, by virtue of the learned clusters, we further propose a contrastive loss function, where the uncensored data in each cluster are set as anchors, and the censored data are treated as positive/negative sample pairs according to whether they belong to the same cluster or not. This design enables the censored data to make full use of the supervision information of the uncensored samples. Through extensive experiments on four popular clinical datasets, we demonstrate that our proposed DSACC achieves advanced performance in terms of both C-index (0.6722, 0.6793, 0.6350, and 0.7943) and Integrated Brier Score (IBS) (0.1616, 0.1826, 0.2028, and 0.1120).