The critical therapist shortage demands scalable training solutions. Standardized Patients, the gold standard, are scarce and costly. Current LLM-based approaches focus on patient simulation for conversational realism but lack pedagogical rigor as Virtual Standardized Patients, lacking faithful reactions to clinical errors and explainable feedback. To bridge this gap, we propose PUPPET, the first neural-symbolic Virtual Standardized Patient governed by an OBSERVE-THINK-BEHAVE architecture. PUPPET externalizes LLM reasoning into a symbolic system where experts implant causal associations between intervention logic (propositional logic) and patient mental states (state machine). This allows PUPPET to behave coherently with controllable and explainable psychological dynamics: intervention logic (OBSERVE) → state transition (THINK) → response (BEHAVE). Our PUPPET-TRAINER further leverages this chain to educate trainees about intervention consequences, standardizing and scaling mental health training. Experiments across three clinical scenarios confirm that PUPPET outperforms baselines in clinical faithfulness and pedagogical value.