This study consists of two parts. The first part (Part 1) is a dose escalation that will enroll subjects with AML or ALL that did not respond or no longer respond to previous standard therapy. The purpose of Part 1 of this research study is to determine the highest dose a patient can tolerate or recommended dose of DS-3201b that can be given to subjects with AML or ALL. Once the highest tolerable dose is determined, additional subjects will be enrolled at that dose into Part 2 of the study.