Grasp detection requires flexibility to handle objects of various shapes without relying on prior object knowledge, while also offering intuitive, user-guided control. In this paper, we introduce GraspSAM, an innovative extension of the Segment Anything Model (SAM) designed for prompt-driven and category-agnostic grasp detection. Unlike previous methods, which are often limited by small-scale training data, Grasp-SAM leverages SAM's large-scale training and prompt-based segmentation capabilities to efficiently support both target-object and category-agnostic grasping. By utilizing adapters, learnable token embeddings, and a lightweight modified decoder, GraspSAM requires minimal fine-tuning to integrate object segmentation and grasp prediction into a unified frame-work. Our model achieves state-of-the-art (SOTA) performance across multiple datasets, including Jacquard, Grasp-Anything, and Grasp-Anything++. Extensive experiments demonstrate GraspSAM's flexibility in handling different types of prompts (such as points, boxes, and language), highlighting its robustness and effectiveness in real-world robotic applications. Robot demonstrations, additional results, and code can be found at https://gistailab.github.io/GraspSAM/.