Accurate segmentation of myocardial scar tissue on late gadolinium enhancement-magnetic cardiac resonance imaging (LGE-CMR) is exceptionally vital for clinical applications, enabling precise diagnosis and effective treatment of various cardiac diseases, such as myocardial infarction and cardiomyopathies. However, the ventricle (LV) variations in the size and shape, artifacts, and image resolution of LGE-CMR has made automatic segmentation of myocardial scar tissue more challenging. While many existing approaches delineate the LV myocardium region using multi-modal segmentation, these models may be computationally complex and suffer from misalignment. Therefore, this study proposed an automatic dual-stage DeepLabV3+ based approach tailored for myocardial scar segmentation on short-axis LGE-MRI exclusively. To segment myocardial scar tissue, the second stage employs the segmented LV chamber from the previous stage. The encoder part of the framework utilizes a MobileNetV2 and ResNet50 backbone for the first and second segmentation, respectively, aiming for optimal resolution of feature maps. Both stages tailor an improved Atrous Spatial Pyramid Pooling module in the DeepLabV3+ model with fine-tuned dilated atrous rates to effectively extract the LV chamber and myocardial scar from the complex LGE-MRI background. Based on the results, the proposed dual-stage network recorded an outstanding segmentation performance, with mean Dice score of 96.02% for LV chamber segmentation and 68.01% for scar tissue extraction.