Key Inclusion Criteria:

1. Participant must be ≥18 years of age
2. Participant must have confirmed diagnosis as follows:

R/R AML and has not achieved adequate response to, cannot tolerate, or refused all approved therapies known to be active for treatment of their disease OR R/R MDS with over 10% blasts in the bone marrow and has not achieved an adequate response to at least 4 cycles of a hypomethylating agent (HMA)- containing regimen or other treatment known to be active for their disease OR R/R AML or R/R MDS that has relapsed after a hematopoietic stem cell transplant (HSCT)
3. Participant must be willing and able to comply with scheduled study visits and treatment plans.
4. Participant must be willing to undergo all study procedures unless contraindicated due to medical risk.
5. Participant must have an Eastern Cooperative Oncology Group (ECOG) performance status (PS) of ≤2
6. Participant must have adequate hepatic function
7. Participant must have adequate renal function
8. Participant must have adequate cardiovascular function
9. Participant must have a white blood cell (WBC) count ≤20 × 10⁹/L (with stable hydroxyurea use allowed)
10. Participant must meet timing requirements with respect to prior therapy and surgery
11. Participant must agree to use effective contraception during the study and for the required post-treatment period: Males: Use condoms (even if vasectomized) during the study and for 90 days post-treatment. Females of childbearing potential: Use a combination of 1 highly effective and 1 effective method of contraception during the study and for 180 days post-treatment.

Key Exclusion Criteria:

1. Participant is unable to provide informed consent and/or to follow protocol requirements.
2. Participant has undergone chimeric antigen receptor T cell therapy or HSCT within 60 days of the first dose of study treatment or has active clinically significant graft-versus-host disease (GVHD)
3. Participant has another malignancy that may interfere with diagnosis and treatment of R/R AML or R/R MDS.
4. Participant has an active severe infection that requires anti-infective therapy or has an unexplained temperature of \>38.5°C during screening visits or on their first day of study treatment.
5. Participant has a known sensitivity to AUTX-703 or any of its components.
6. Participant is taking systemic strong CYP3A4 inhibitors or inducers within 14 days of the first dose of study treatment.
7. Participant who are taking proton pump inhibitors should be switched to another acid-reducing agent such as an antacid or H2 blocker
8. Participant is taking P-gp and breast cancer resistance protein (BCRP) inhibitors or inducers within 14 days of first dose of study treatment.
9. Participant has active hepatitis B virus (HBV) or hepatitis C virus (HCV) infections with detectable viral load
10. Participant has experienced AIDS related illness within the past 6 months or have detectable HIV viral load.
11. Participant has an uncontrolled intercurrent illness
12. Participant has active Class III or IV cardiovascular disease within 6 months prior to the start of study treatment
13. Participant is unable to tolerate the administration of oral medication or has GI dysfunction that would preclude adequate absorption, distribution, metabolism, or excretion of an oral medication
14. Participant is pregnant or breastfeeding or is planning to become pregnant within 1 year of the start of study treatment