Douglas "Mike" Day Psychedelic Therapy to Save Lives Act of 2023 This bill requires the Department of Defense (DOD) to award grants to eligible entities to research the treatment of certain members of the Armed Forces through the use of specified psychedelic substances (e.g., MDMA). Specifically, the research must focus on members of the Armed Forces who are serving on active duty and have been diagnosed with post-traumatic stress, a traumatic brain injury, or chronic traumatic encephalopathy. Under the bill, eligible entities include federal or state government entities, academic institutions, and nonprofit entities.