3D Affordance detection is a challenging problem with broad applications on various robotic tasks. Existing methods typically formulate the detection paradigm as a label-based semantic segmentation task. This paradigm relies on predefined labels and lacks the ability to comprehend complex natural language, resulting in limited generalization in open-world scene. To address these limitations, we reformulate the traditional affordance detection paradigm into \textit{Instruction Reasoning Affordance Segmentation} (IRAS) task. This task is designed to output a affordance mask region given a query reasoning text, which avoids fixed categories of input labels. We accordingly propose the \textit{3D-AffordanceLLM} (3D-ADLLM), a framework designed for reasoning affordance detection in 3D open-scene. Specifically, 3D-ADLLM introduces large language models (LLMs) to 3D affordance perception with a custom-designed decoder for generating affordance masks, thus achieving open-world reasoning affordance detection. In addition, given the scarcity of 3D affordance datasets for training large models, we seek to extract knowledge from general segmentation data and transfer it to affordance detection. Thus, we propose a multi-stage training strategy that begins with a novel pre-training task, i.e., \textit{Referring Object Part Segmentation}~(ROPS). This stage is designed to equip the model with general recognition and segmentation capabilities at the object-part level. Then followed by fine-tuning with the IRAS task, 3D-ADLLM obtains the reasoning ability for affordance detection. In summary, 3D-ADLLM leverages the rich world knowledge and human-object interaction reasoning ability of LLMs, achieving approximately an 8\% improvement in mIoU on open-vocabulary affordance detection tasks.