This is a single arm, dose escalation/ de-escalation, single US center, unblinded, phase 1 study. Its main goal is to determine the safety and tolerability of the autologous genetically modified T cell (BPX-701) in subjects with relapsed or refractory AML or advanced hypomethylating agent-resistant MDS. Rimiducid (AP1903) will be administrated treat uncontrolled BPX-701 toxicity, such as Cytokine Release Syndrome or severe off-tumor/on-target toxicities.