Understanding what deep learning (DL) models learn is essential for the safe deployment of artificial intelligence (AI) in clinical settings. While previous work has focused on pixel-based explainability methods, less attention has been paid to the textual concepts learned by these models, which may better reflect the reasoning used by clinicians. We introduce Mammo-CLIP Dissect, the first concept-based explainability framework for systematically dissecting DL vision models trained for mammography. Leveraging a mammography-specific vision-language model (Mammo-CLIP) as a "dissector," our approach labels neurons at specified layers with human-interpretable textual concepts and quantifies their alignment to domain knowledge. Using Mammo-CLIP Dissect, we investigate three key questions: (1) how concept learning differs between DL vision models trained on general image datasets versus mammography-specific datasets; (2) how fine-tuning for downstream mammography tasks affects concept specialisation; and (3) which mammography-relevant concepts remain underrepresented. We show that models trained on mammography data capture more clinically relevant concepts and align more closely with radiologists' workflows than models not trained on mammography data. Fine-tuning for task-specific classification enhances the capture of certain concept categories (e.g., benign calcifications) but can reduce coverage of others (e.g., density-related features), indicating a trade-off between specialisation and generalisation. Our findings show that Mammo-CLIP Dissect provides insights into how convolutional neural networks (CNNs) capture mammography-specific knowledge. By comparing models across training data and fine-tuning regimes, we reveal how domain-specific training and task-specific adaptation shape concept learning. Code and concept set are available: https://github.com/Suaiba/Mammo-CLIP-Dissect.