Object detection methods have evolved from closed-set to open-set paradigms over the years. Current open-set object detectors, however, remain constrained by their exclusive reliance on positive indicators based on given prompts like text descriptions or visual exemplars. This positive-only paradigm experiences consistent vulnerability to visually similar but semantically different distractors. We propose T-Rex-Omni, a novel framework that addresses this limitation by incorporating negative visual prompts to negate hard negative distractors. Specifically, we first introduce a unified visual prompt encoder that jointly processes positive and negative visual prompts. Next, a training-free Negating Negative Computing (NNC) module is proposed to dynamically suppress negative responses during the probability computing stage. To further boost performance through fine-tuning, our Negating Negative Hinge (NNH) loss enforces discriminative margins between positive and negative embeddings. T-Rex-Omni supports flexible deployment in both positive-only and joint positive-negative inference modes, accommodating either user-specified or automatically generated negative examples. Extensive experiments demonstrate remarkable zero-shot detection performance, significantly narrowing the performance gap between visual-prompted and text-prompted methods while showing particular strength in long-tailed scenarios (51.2 AP_r on LVIS-minival). This work establishes negative prompts as a crucial new dimension for advancing open-set visual recognition systems.