Large language models (LLMs) show promise in automating clinical diagnosis, yet their non-transparent decision-making and limited alignment with diagnostic standards hinder trust and clinical adoption. We address this challenge by proposing a two-stage diagnostic framework that enhances transparency, trustworthiness, and reliability. First, we introduce Evidence-Guided Diagnostic Reasoning (EGDR), which guides LLMs to generate structured diagnostic hypotheses by interleaving evidence extraction with logical reasoning grounded in DSM-5 criteria. Second, we propose a Diagnosis Confidence Scoring (DCS) module that evaluates the factual accuracy and logical consistency of generated diagnoses through two interpretable metrics: the Knowledge Attribution Score (KAS) and the Logic Consistency Score (LCS). Evaluated on the D4 dataset with pseudo-labels, EGDR outperforms direct in-context prompting and Chain-of-Thought (CoT) across five LLMs. For instance, on OpenBioLLM, EGDR improves accuracy from 0.31 (Direct) to 0.76 and increases DCS from 0.50 to 0.67. On MedLlama, DCS rises from 0.58 (CoT) to 0.77. Overall, EGDR yields up to +45% accuracy and +36% DCS gains over baseline methods, offering a clinically grounded, interpretable foundation for trustworthy AI-assisted diagnosis.