This study will evaluate patients with relapsed or refractory Acute Myeloid Leukemia (AML) or advanced hypomethylating agent-resistant myelodysplastic syndrome (MDS) who will have autologous immune cells, called T cells, collected via apheresis. The T cells will be reinfused according to a dose-finding schedule after the patient has been identified as having adequate lymphopenia to provide for homeostatic expansion of the adoptively transferred, engineered T cell therapeutic product. As a safety measure, these T cells have been programmed with a self-destruct switch so that they can be destroyed if they start to react against tissues (Graft versus host disease).