Imitation learning for robotic grasping is often plagued by the multimodal problem: when a scene contains multiple valid targets, demonstrations of grasping different objects create conflicting training signals. Standard imitation learning policies fail by averaging these distinct actions into a single, invalid action. In this paper, we introduce SAM2Grasp, a novel framework that resolves this issue by reformulating the task as a uni-modal, prompt-conditioned prediction problem. Our method leverages the frozen SAM2 model to use its powerful visual temporal tracking capability and introduces a lightweight, trainable action head that operates in parallel with its native segmentation head. This design allows for training only the small action head on pre-computed temporal-visual features from SAM2. During inference, an initial prompt, such as a bounding box provided by an upstream object detection model, designates the specific object to be grasped. This prompt conditions the action head to predict a unique, unambiguous grasp trajectory for that object alone. In all subsequent video frames, SAM2's built-in temporal tracking capability automatically maintains stable tracking of the selected object, enabling our model to continuously predict the grasp trajectory from the video stream without further external guidance. This temporal-prompted approach effectively eliminates ambiguity from the visuomotor policy. We demonstrate through extensive experiments that SAM2Grasp achieves state-of-the-art performance in cluttered, multi-object grasping tasks.