Cancer cells and pathogens can evade T cell receptors (TCRs) via mutations in immunogenic epitopes. TCR cross-reactivity (i.e., recognition of multiple epitopes with sequence similarities) can counteract such escape but may cause severe side effects in cell-based immunotherapies through targeting self-antigens. To predict the effect of epitope point mutations on T cell functionality, we here present the random forest-based model Predicting T Cell Epitope-Specific Activation against Mutant Versions (P-TEAM). P-TEAM was trained and tested on three datasets with TCR responses to single-amino-acid mutations of the model epitope SIINFEKL, the tumor neo-epitope VPSVWRSSL, and the human cytomegalovirus antigen NLVPMVATV, totaling 9,690 unique TCR-epitope interactions. P-TEAM was able to accurately classify T cell reactivities and quantitatively predict T cell functionalities for unobserved single-point mutations and unseen TCRs. Overall, P-TEAM provides an effective computational tool to study T cell responses against mutated epitopes.