Individuals with schizophrenia experience significant cognitive impairments and alterations in brain function. However, the shared and unique brain functional patterns underlying cognition deficits and symptom severity in schizophrenia remain poorly understood. We design an interpretable graph-based multi-task deep learning framework to enhance the simultaneous prediction of schizophrenia illness severity and cognitive functioning measurements by using functional connectivity, and identify both shared and unique brain patterns associated with these phenotypes on 378 subjects from three datasets. Our framework outperforms both single-task and state-of-the-art multi-task learning methods in predicting four Positive and Negative Syndrome Scale (PANSS) subscales and four cognitive domain scores. The performance is replicable across three datasets, and the shared and unique functional changes are confirmed by meta-analysis at both regional and modular levels. Our study provides insights into the neural correlates of illness severity and cognitive implications, offering potential targets for further evaluations of treatment effects and longitudinal follow-up.