The surge in rich multimodal content on social media platforms has greatly advanced Multimodal Sentiment Analysis (MSA), with Large Language Models (LLMs) further accelerating progress in this field. Current approaches primarily leverage the knowledge and reasoning capabilities of parameter-heavy (Multimodal) LLMs for sentiment classification, overlooking autonomous multimodal sentiment reasoning generation in resource-constrained environments. Therefore, we focus on the Resource-Limited Joint Multimodal Sentiment Reasoning and Classification task, JMSRC, which simultaneously performs multimodal sentiment reasoning chain generation and sentiment classification only with a lightweight model. We propose a Multimodal Chain-of-Thought Reasoning Distillation model, MulCoT-RD, designed for JMSRC that employs a "Teacher-Assistant-Student" distillation paradigm to address deployment constraints in resource-limited environments. We first leverage a high-performance Multimodal Large Language Model (MLLM) to generate the initial reasoning dataset and train a medium-sized assistant model with a multi-task learning mechanism. A lightweight student model is jointly trained to perform efficient multimodal sentiment reasoning generation and classification. Extensive experiments on four datasets demonstrate that MulCoT-RD with only 3B parameters achieves strong performance on JMSRC, while exhibiting robust generalization and enhanced interpretability.