Methods for the ex vivo use of NAD to remove T cells that can potentially cause graft-verus-host disease (GvHD) from hematopoietic stem cell sources. Hematopoietic stem cell sources include bone marrow, cord blood, and peripheral blood (including mobilized peripheral blood). The present invention is a method including steps for using the hematopoietic stem cell sources treated with NAD for hematopoietic stem cell transplants (HSCTs). HSCTs are used as the standard-of-care in many diseases including several types of cancer and several genetic disorders. The majority of these transplants are allogeneic, in which the stem cell source comes from a donor who is a different individual than the intended recipient. Allogeneic HSCTs carry a risk of causing GvHD, in which donor T cells attack the recipient.