Neoantigens derived from somatic mutations are specific to cancer cells and are ideal targets for cancer immunotherapy. KRAS is the most frequently mutated oncogene and drives the pathogenesis of several cancers. Here we show the identification and development of an affinity-enhanced T cell receptor (TCR) that recognizes a peptide derived from the most common KRAS mutant, KRAS^G12D, presented in the context of HLA-A*11:01. The affinity of the engineered TCR is increased by over one million-fold yet fully able to distinguish KRAS^G12D over KRAS^WT. While crystal structures reveal few discernible differences in TCR interactions with KRAS^WT versus KRAS^G12D, thermodynamic analysis and molecular dynamics simulations reveal that TCR specificity is driven by differences in indirect electrostatic interactions. The affinity enhanced TCR, fused to a humanized anti-CD3 scFv, enables selective killing of cancer cells expressing KRAS^G12D. Our work thus reveals a molecular mechanism that drives TCR selectivity and describes a soluble bispecific molecule with therapeutic potential against cancers harboring a common shared neoantigen.