Quantifying accurate functional magnetic resonance imaging (fMRI) activation maps can be dampened by spatio‐temporally varying task‐correlated motion (TCM) artifacts in certain task paradigms (e.g., overt speech). Such real‐world tasks are relevant to characterize longitudinal brain reorganization poststroke, and removal of TCM artifacts is vital for improved clinical interpretation and translation. In this study, we developed a novel independent component analysis (ICA)‐based approach to denoise spatio‐temporally varying TCM artifacts in 14 persons with aphasia who participated in an overt language fMRI paradigm. We compared the new methodology with other existing approaches such as “standard” volume registration, nonselective motion correction ICA packages (i.e., AROMA), and combining the novel approach with AROMA. Results show that the proposed methodology outperforms other approaches in removing TCM‐related false positive activity (i.e., improved detectability power) with high spatial specificity. The proposed method was also effective in maintaining a balance between removal of TCM‐related trial‐by‐trial variability and signal retention. Finally, we show that the TCM artifact is related to clinical metrics, such as speech fluency and aphasia severity, and the implication of TCM denoising on such relationship is also discussed. Overall, our work suggests that routine bulkhead motion based denoising packages cannot effectively account for spatio‐temporally varying TCM. Further, the proposed TCM denoising approach requires a one‐time front‐end effort to hand label and train the classifiers that can be cost‐effectively utilized to denoise large clinical data sets.