Chain-of-thought Distillation (CoTD) aims at distilling Chain-of-thought (CoT) reasoning ability of large language models (LLMs) to much smaller student models. The core of CoTD is using a large teacher model to generate rationales and fine-tune smaller student models. However, current Chain-of-thought Distillation works have the following limitations: 1) Student models are separately distilled from specific reasoning tasks and lack a collaboration mechanism, hindering the enhancement of reasoning performance through collaboration among various reasoning tasks. 2) The parameter update of student models severely harms the CoT reasoning ability on other unseen reasoning tasks not included in the distillation process. In this work, we introduce a novel CoT Distillation method, MoDE-CoTD, which decouples the CoT reasoning abilities out of the student model by distilling multiple LoRA-Experts and freezing the parameters of the student model. Sequentially, LoRA-Experts are combined and adapted to handle both seen and unseen reasoning tasks, enabling collaboration among diverse reasoning tasks to further enhance CoT reasoning performance. Experimental results on 14 datasets (including 4 unseen datasets) demonstrate the strength of MoDE-CoTD, with an average accuracy gain of 6.3% on seen datasets and 7.8% on unseen datasets.