Whole-Slide Histopathology Image (WSI) is generally considered the gold standard for cancer diagnosis and prognosis. Given the large inter-operator variation among pathologists, there is an imperative need to develop machine learning models based on WSIs for consistently predicting patient prognosis. The existing WSI-based prediction methods do not utilize the ordinal ranking loss to train the prognosis model, and thus cannot model the strong ordinal information among different patients in an efficient way. Another challenge is that a WSI is of large size (e.g., 100,000-by-100,000 pixels) with heterogeneous patterns but often only annotated with a single WSI-level label, which further complicates the training process. To address these challenges, we consider the ordinal characteristic of the survival process by adding a ranking-based regularization term on the Cox model and propose a weakly supervised deep ordinal Cox model (BDOCOX) for survival prediction from WSIs. Here, we generate amounts of bags from WSIs, and each bag is comprised of the image patches representing the heterogeneous patterns of WSIs, which is assumed to match the WSI-level labels for training the proposed model. The effectiveness of the proposed method is well validated by theoretical analysis as well as the prognosis and patient stratification results on three cancer datasets from The Cancer Genome Atlas (TCGA).