We propose an automated, explainable artificial intelligence (xAI) system for age-related macular degeneration (AMD) diagnosis. Mimicking the physician's perceptions, the proposed xAI system is capable of deriving clinically meaningful features from optical coherence tomography (OCT) B-scan images to differentiate between a normal retina, different grades of AMD (early, intermediate, geographic atrophy (GA), inactive wet or active neovascular disease [exudative or wet AMD]), and non-AMD diseases. Particularly, we extract retinal OCT-based clinical imaging markers that are correlated with the progression of AMD, which include: (i) subretinal tissue, sub-retinal pigment epithelial tissue, intraretinal fluid, subretinal fluid, and choroidal hypertransmission detection using a DeepLabV3+ network; (ii) detection of merged retina layers using a novel convolutional neural network model; (iii) drusen detection based on 2D curvature analysis; (iv) estimation of retinal layers' thickness, and first-order and higher-order reflectivity features. Those clinical features are used to grade a retinal OCT in a hierarchical decision tree process. The first step looks for severe disruption of retinal layers' indicative of advanced AMD. These cases are analyzed further to diagnose GA, inactive wet AMD, active wet AMD, and non-AMD diseases. Less severe cases are analyzed using a different pipeline to identify OCT with AMD-specific pathology, which is graded as intermediate-stage or early-stage AMD. The remainder is classified as either being a normal retina or having other non-AMD pathology. The proposed system in the multi-way classification task, evaluated on 1285 OCT images, achieved 90.82% accuracy. These promising results demonstrated the capability to automatically distinguish between normal eyes and all AMD grades in addition to non-AMD diseases.