CD70 is an attractive target for chimeric antigen receptor (CAR) T-cell therapy for the treatment of both solid and liquid malignancies. However, the functionality of CD70-specific CAR T cells is modest. We optimized a CD70-specific VHH-based CAR (nanoCAR). We evaluated the nanoCARs in clinically relevant models in vitro, using co-cultures of CD70-specific nanoCAR T cells with malignant rhabdoid tumor organoids, and in vivo, using a diffuse large B-cell lymphoma patient-derived xenograft (PDX) model. Although the nanoCAR T cells were highly efficient in organoid co-cultures, they showed only modest efficacy in the PDX model. We determined that fratricide was not causing this loss in efficacy but rather CD70 interaction in cis with the nanoCAR-induced exhaustion. Knocking out CD70 in nanoCAR T cells using CRISPR/Cas9 resulted in dramatically enhanced functionality in the diffuse large B-cell lymphoma PDX model. Through single-cell transcriptomics, we obtained evidence that CD70 knockout CD70-specific nanoCAR T cells were protected from antigen-induced exhaustion. In addition, we demonstrated that wild-type CD70-specific nanoCAR T cells already exhibited signs of exhaustion shortly after production. Their gene signature strongly overlapped with gene signatures of exhausted CAR T cells. Conversely, the gene signature of knockout CD70-specific nanoCAR T cells overlapped with the gene signature of CAR T-cell infusion products leading to complete responses in chronic lymphatic leukemia patients. Our data show that CARs targeting endogenous T-cell antigens negatively affect CAR T-cell functionality by inducing an exhausted state, which can be overcome by knocking out the specific target.