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Presently, breast cancer is considered as a major health problem among women over the globe. The identification of breast cancer in the beginning stage can decrease the mortality rate to a considerable extent. Mammogram is an effective and commonly used technique for the detection and screening of breast cancer. The advanced deep learning (DL) techniques are utilized by radiologists for accurate detection and classification of medical images. This paper develops a new deep segmentation with residual network (DS-RN) based breast cancer diagnosis model using mammogram images.The presented DS-RN model involves preprocessing, Faster Region based Convolution Neural Network (R-CNN) (Faster R-CNN) with Inception v2 model based segmentation, feature extraction and classification. To classify the mammogram images, decision tree (DT) and random forest (RF) classifier models are used. A detailed simulation process is performed to ensure the betterment of the presented model on the Mini-MIAS dataset. The obtained experimental values stated that the DS-RN model has reached to a maximum classification performance with the maximum sensitivity, specificity, accuracy and F-Measure of 98.15%, 100%, 98.86% and 99.07% respectively.