Humour translation plays a vital role as a bridge between different cultures, fostering understanding and communication. Although most existing Large Language Models (LLMs) are capable of general translation tasks, these models still struggle with humour translation, which is especially reflected through linguistic interference and lacking humour in translated text. In this paper, we propose a psychology-inspired Humour Decomposition Mechanism (HDM) that utilises Chain-of-Thought (CoT) to imitate the ability of the human thought process, stimulating LLMs to optimise the readability of translated humorous texts. Moreover, we integrate humour theory in HDM to further enhance the humorous elements in the translated text. Our automatic evaluation experiments on open-source humour datasets demonstrate that our method significantly improves the quality of humour translation, yielding average gains of 7.75% in humour, 2.81% in fluency, and 6.13% in coherence of the generated text.