As large language models (LLMs) have demonstrated impressive multiple step-by-step reasoning capabilities in recent natural language processing (NLP) reasoning tasks, many studies are interested in distilling reasoning abilities into smaller language models (SLMs) via fine-tuning. Previous distillation methods usually utilize the capabilities of LLMs to generate chain-of-thought (CoT) samples to teach SLMs. However, this distillation approach performs poorly in certain scenarios due to the limitations of CoT. In this work, we introduce a novel Mixed Distillation (MD) framework, distilling multiple step-by-step reasoning abilities into SLMs. First, we leverage LLMs to generate multiple step-by-step reasoning rationales by sampling automatically. Then, we create high-quality, well-balanced mixed thought data and design a novel multi-task loss to help SLMs better learn and adaptively activate multiple step-by-step reasoning. Our extensive experiments demonstrate that MD enhances both single-path (using either CoT or PoT) and multi-path (using both CoT and PoT) reasoning abilities of SLMs during inference across reasoning tasks. Notably, a single model generated by MD exceeds the comprehensive performance of an ensemble of two individual CoT and PoT distilled models. Mistral-7B using MD can achieve remarkable improvements of 87.5%, 74.0% and 77.1% on SVAMP, GSM8K and ASDIV, respectively, outperforming the teacher model, GPT-3.5-Turbo. We hope our work provides insight into SLMs’ multiple step-by-step reasoning abilities.