Interactive 3D segmentation in radiance fields is crucial for advanced 3D scene understanding and manipulation. However, existing methods often struggle to achieve both volumetric completeness and segmentation accuracy, primarily because they fail to consider the critical links between 2D prompt-based segmentations across multiple views. Motivated by this gap, we introduce Gaussian Prompter, a novel approach specifically designed for 3D Gaussian Splatting. The core idea behind Gaussian Prompter is to seamlessly integrate a Gaussian-centric segmentation paradigm by effectively linking various 2D prompts from multi-view segmentations to ensure consistent 3D segmentation. To realize this, we employ two tailored approaches: GaussBlend and PinPrompt. GaussBlend aggregates multi-view 2D segmentation masks into a cohesive 3D segmentation, ensuring both accuracy and completeness. PinPrompt leverages high-confidence prompts from adjacent views to enhance segmentation precision further. Additionally, to address the lack of complex datasets in 3D segmentation, we introduce the SegMip-360 dataset, which includes over 350 precisely annotated masks across seven scenes. Extensive experiments demonstrate that the Gaussian Prompter significantly outperforms state-of-the-art methods in both segmentation accuracy and completeness. Our code and video demonstrations can be found at our repository and project page.