Objective. Effective fusion of histology slides and molecular profiles from genomic data has shown great potential in the diagnosis and prognosis of gliomas. However, it remains challenging to explicitly utilize the consistent-complementary information among different modalities and create comprehensive representations of patients. Additionally, existing researches mainly focus on complete multi-modality data and usually fail to construct robust models for incomplete samples. Approach. In this paper, we propose a dual-space disentangled-multimodal network (DDM-net) for glioma diagnosis and prognosis. DDM-net disentangles the latent features generated by two separate variational autoencoders (VAEs) into common and specific components through a dual-space disentangled approach, facilitating the construction of comprehensive representations of patients. More importantly, DDM-net imputes the unavailable modality in the latent feature space, making it robust to incomplete samples. Main results. We evaluated our approach on the TCGA-GBMLGG dataset for glioma grading and survival analysis tasks. Experimental results demonstrate that the proposed method achieves superior performance compared to state-of-the-art methods, with a competitive AUC of 0.952 and a C-index of 0.768. Significance. The proposed model may help the clinical understanding of gliomas and can serve as an effective fusion model with multimodal data. Additionally, it is capable of handling incomplete samples, making it less constrained by clinical limitations.