Research on text simplification has primarily focused on lexical and sentence-level changes. Long document-level simplification (DS) is still relatively unexplored. Large Language Models (LLMs), like ChatGPT, have excelled in many natural language processing tasks. However, their performance on DS tasks is unsatisfactory, as they often treat DS as merely document summarization. For the DS task, the generated long sequences not only must maintain consistency with the original document throughout, but complete moderate simplification operations encompassing discourses, sentences, and word-level simplifications. Human editors employ a hierarchical complexity simplification strategy to simplify documents. This study delves into simulating this strategy through the utilization of a multi-stage collaboration using LLMs. We propose a progressive simplification method (ProgDS) by hierarchically decomposing the task, including the discourse-level, topic-level, and lexical-level simplification. Experimental results demonstrate that ProgDS significantly outperforms existing smaller models or direct prompting with LLMs, advancing the state-of-the-art in the document simplification task.