Timely and accurate diagnosis of neurodegenerative disorders, such as Alzheimer's disease, is central to disease management. Existing deep learning models require large-scale annotated datasets and often function as "black boxes". Additionally, datasets in clinical practice are frequently small or unlabeled, restricting the full potential of deep learning methods. Here, we introduce REMEMBER -- Retrieval-based Explainable Multimodal Evidence-guided Modeling for Brain Evaluation and Reasoning -- a new machine learning framework that facilitates zero- and few-shot Alzheimer's diagnosis using brain MRI scans through a reference-based reasoning process. Specifically, REMEMBER first trains a contrastively aligned vision-text model using expert-annotated reference data and extends pseudo-text modalities that encode abnormality types, diagnosis labels, and composite clinical descriptions. Then, at inference time, REMEMBER retrieves similar, human-validated cases from a curated dataset and integrates their contextual information through a dedicated evidence encoding module and attention-based inference head. Such an evidence-guided design enables REMEMBER to imitate real-world clinical decision-making process by grounding predictions in retrieved imaging and textual context. Specifically, REMEMBER outputs diagnostic predictions alongside an interpretable report, including reference images and explanations aligned with clinical workflows. Experimental results demonstrate that REMEMBER achieves robust zero- and few-shot performance and offers a powerful and explainable framework to neuroimaging-based diagnosis in the real world, especially under limited data.