Inclusion Criteria:

* Age ≥ 18 years as MDS and MDS/MPN are a very rare disease in the pediatric setting.
* Diagnosis of MDS or MDS/MPN (including CMML, aCML, MDS/MPN-U) according to WHO and:

* Initial phase 1 cohorts (cohorts A): MDS participants with no response after 4 cycles of azacitidine, decitabine, guadecitabine, CC-486 or ASTX727 or relapse or progression after any number of cycles OR MDS/MPN relapsed/refractory following treatment with hydroxyurea OR at least 4 cycles of azacytidine, decitabine, guadecitabine or ASTX727 or relapse or progression after any number of cycles or who are intolerant of treatment with hydroxiurea.
* Phase 2 dose expansion cohort:
* Relapsed MDS cohort (Cohort B): no response after 4 cycles of azacitidine, decitabine, guadecitabine or ASTX727 or relapse or progression after any number of cycles.
* Relapsed MDS/MPN cohort (Cohort C): relapsed/refractory following treatment with hydroxyurea or at least 4 cycles of azacytidine, decitabine, guadecitabine or ASTX727 or relapse or progression after any number of cycles or who are intolerant of treatment with wih hydroxiurea.
* Known mutation in genes leading to RAS pathway activation (NRAS, KRAS, BRAF, CBL, NF1, PTPN11).
* Creatinine clearance ≥30ml/min based on the Cockcroft-Gault Glomerular Filtration Rate estimation.
* Adequate hepatic function with total bilirubin ≤1.5x ULN, AST or ALT ≤3 xULN.
* ECOG Performance Status 0-2.
* Participant (or patient's legally authorized representative) must have signed an informed consent document indicating that the participant understands the purpose of and procedures required for the study and is willing to participate in the study. Non-English speaking participants may be consented.
* Prior hydroxyurea for control of leukocytosis or use of hematopoietic growth factors (eg, G-CSF, GM-CSF, procrit, aranesp, thrombopoietins) is allowed at any time prior to cycle 1 day 1 of therapy.
* For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated.
* Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. For participants with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load.
* Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. The effects of ASTX029 on the developing human fetus are unknown. For this reason and because other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. (Refer to Pregnancy Assessment Policy MD Anderson Institutional Policy # CLN1114). This includes all female participants, between the onset of menses (as early as 8 years of age) and 55 years unless the participant presents with an applicable exclusionary factor which may be one of the following:

* Postmenopausal (no menses in greater than or equal to 12 consecutive months).
* History of hysterectomy or bilateral salpingo-oophorectomy.
* Ovarian failure (Follicle Stimulating Hormone and Estradiol in menopausal range, who have received Whole Pelvic Radiation Therapy).
* History of bilateral tubal ligation or another surgical sterilization procedure.
* Approved methods of birth control are as follows: Hormonal contraception (i.e. birth control pills, injection, implant, transdermal patch, vaginal ring), Intrauterine device (IUD), Tubal Ligation or hysterectomy, Subject/Partner post vasectomy, Implantable or injectable contraceptives, and condoms plus spermicide. Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however periodic abstinence, the rhythm method, and the withdrawal method are not acceptable methods of birth control. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately.
* Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of ASTX727 and ASTX029 administration.
* Ability to understand and the willingness to sign a written informed consent document.

Exclusion Criteria:

* Participants who are currently receiving treatment for a malignancy (not including basal cell carcinoma, nonmelanoma skin cancer, cervical carcinoma in situ, early stage breast cancer or localized prostate cancer treated with hormone therapy). Participants with history of other cancers should be free of disease for at least 2 years prior to the Screening Visit or not requiring active treatment at the time of enrollment.
* Participants who are receiving any other investigational agents.
* Participants who have an active, life-threatening, or clinically-significant uncontrolled systemic infection requiring hospitalization.
* Participants who have a known malabsorption syndrome or other condition that may impair absorption of study medication (e.g., gastrectomy).
* Pregnant women are excluded from this study because ASTX029 and ASTX727 are agents with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with these agents, breastfeeding should be discontinued if the mother is treated on study. These potential risks may also apply to other agents used in this study.
* Participants with reproductive potential who are unwilling to following contraception requirements (including condom use for males with sexual partners, and for females: prescription oral contraceptives \[birth control pills\], contraceptive injections, intrauterine devices \[IUD\], double-barrier method \[spermicidal jelly or foam with condoms or diaphragm\], contraceptive patch, or surgical sterilization) throughout the study.
* Female participants with reproductive potential who do not have a negative urine or blood beta-human chorionic gonadotropin (beta HCG) pregnancy test at screening.
* Participants receiving any other concurrent investigational agent or chemotherapy, radiotherapy, or immunotherapy within 7 days of therapy initiation.
* Participants known to be positive for hepatitis B surface antigen expression or with active hepatitis C infection (positive by polymerase chain reaction or on antiviral therapy for hepatitis C within the last 6 months).
* Participants with history of HIV with CD4+ T-cell (CD4+) counts \<350 cell/mcL or with AIDS-defining opportunistic infections in the last 12 months are also excluded. Participants with well controlled HIV (defined as CD4+ counts \>350 cells/mcL with undetectable viral load prior to enrollment with no AIDS-defining opportunistic infections in the past 12 months) on therapy with antiretroviral therapies known to be metabolites of cytochrome P450 (CYP3A4) enzymes will also be excluded.
* Participants with QTc interval \>480 msec based on average of triplicate ECG readings at the Screening Visit using the Fridericia formula (QTcF), with the exception of participants with right bundle branch block or left bundle branch block.
* New York Heart Association (NYHA) Class III or IV congestive heart failure or LVEF \<50 by echocardiogram or multigated acquisition (MUGA) scan.
* History of myocardial infarction within the last 6 months or unstable/uncontrolled angina pectoris or history of severe and/or uncontrolled ventricular arrhythmias.
* Participants with psychiatric illness/social situations that would limit compliance with study requirements.