Background: Diagnosing breast cancer masses and calcification clusters have paramount significance in mammography, which aids in mitigating the disease’s complexities and curing it at early stages. However, a wrong mammogram interpretation may lead to an unnecessary biopsy of the false-positive findings, which reduces the patient’s survival chances. Consequently, approaches that learn to discern breast masses can reduce the number of misconceptions and incorrect diagnoses. Conventionally used classification models focus on feature extraction techniques specific to a particular problem based on domain information. Deep learning strategies are becoming promising alternatives to solve the many challenges of feature-based approaches. Methods: This study introduces a convolutional neural network (ConvNet)-based deep learning method to extract features at varying densities and discern mammography’s normal and suspected regions. Two different experiments were carried out to make an accurate diagnosis and classification. The first experiment consisted of five end-to-end pre-trained and fine-tuned deep convolution neural networks (DCNN). The in-depth features extracted from the ConvNet are also used to train the support vector machine algorithm to achieve excellent performance in the second experiment. Additionally, DCNN is the most frequently used image interpretation and classification method, including VGGNet, GoogLeNet, MobileNet, ResNet, and DenseNet. Moreover, this study pertains to data cleaning, preprocessing, and data augmentation, and improving mass recognition accuracy. The efficacy of all models is evaluated by training and testing three mammography datasets and has exhibited remarkable results. Results: Our deep learning ConvNet+SVM model obtained a discriminative training accuracy of 97.7% and validating accuracy of 97.8%, contrary to this, VGGNet16 method yielded 90.2%, 93.5% for VGGNet19, 63.4% for GoogLeNet, 82.9% for MobileNetV2, 75.1% for ResNet50, and 72.9% for DenseNet121. Conclusions: The proposed model’s improvement and validation are appropriated in conventional pathological practices that conceivably reduce the pathologist’s strain in predicting clinical outcomes by analyzing patients’ mammography images.