Large language models (LLMs) exhibit exceptional performance but pose inherent risks of generating toxic content, restricting their safe deployment. While traditional methods (e.g., alignment) adjust output preferences, they fail to eliminate underlying toxic regions in parameters, leaving models vulnerable to adversarial attacks. Prior mechanistic studies characterize toxic regions as "toxic vectors" or "layer-wise subspaces", yet our analysis identifies critical limitations: i) Removed toxic vectors can be reconstructed via linear combinations of non-toxic vectors, demanding targeting of entire toxic subspace; ii) Contrastive objective over limited samples inject noise into layer-wise subspaces, hindering stable extraction. These highlight the challenge of identifying robust toxic subspace and removing them. Therefore, we propose GLOSS (GLobal tOxic Subspace Suppression), a lightweight method that mitigates toxicity by identifying and eliminating this global subspace from FFN parameters. Experiments on LLMs (e.g., Qwen3) show GLOSS achieves SOTA detoxification while preserving general capabilities without requiring large-scale retraining. WARNING: This paper contains context which is toxic in nature.