Existing bias mitigation methods require social-group-specific word pairs (e.g., “man” – “woman”) for each social attribute (e.g., gender), restricting the bias mitigation to only one specified social attribute. Further, this constraint renders such methods impractical and costly for mitigating bias in understudied and/or unmarked social groups. We propose that the Stereotype Content Model (SCM) — a theoretical framework developed in social psychology for understanding the content of stereotyping — can help debiasing efforts to become social-group-agnostic by capturing the underlying connection between bias and stereotypes. SCM proposes that the content of stereotypes map to two psychological dimensions of warmth and competence. Using only pairs of terms for these two dimensions (e.g., warmth: “genuine” – “fake”; competence: “smart” – “stupid”), we perform debiasing with established methods on both pre-trained word embeddings and large language models. We demonstrate that our social-group-agnostic, SCM-based debiasing technique performs comparably to group-specific debiasing on multiple bias benchmarks, but has theoretical and practical advantages over existing approaches.