Contrastively trained vision-language models have achieved remarkable progress in vision and language representation learning, leading to state-of-the-art models for various downstream multimodal tasks. However, recent research has highlighted severe limitations of these models in their ability to perform compositional reasoning over objects, attributes, and relations. Scene graphs have emerged as an effective way to understand images compositionally. These are graph-structured semantic representations of images that contain objects, their attributes, and relations with other objects in a scene. In this work, we consider the scene graph parsed from text as a proxy for the image scene graph and propose a graph decomposition and augmentation framework along with a coarse-to-fine contrastive learning objective between images and text that aligns sentences of various complexities to the same image. Along with this, we propose novel negative mining techniques in the scene graph space for improving attribute binding and relation understanding. Through extensive experiments, we demonstrate the effectiveness of our approach that significantly improves attribute binding, relation understanding, systematic generalization, and productivity on multiple recently proposed benchmarks (For example, improvements upto $18\%$ for systematic generalization, $16.5\%$ for relation understanding over a strong baseline), while achieving similar or better performance than CLIP on various general multimodal tasks.