Inclusion Criteria:
* Signed informed consent must be obtained prior to participation in the study
* Age ≥ 18 years at the date of signing the informed consent form (ICF)
* Morphologically confirmed diagnosis of the following based on 2016 World Health Organization (WHO) classification (Arber et al 2016): Phase 1b, patients with relapsed or refractory of any of the following; phase 2, patients with newly diagnosed of any of the following:
* Chronic myelomonocytic leukemia (CMML), classified as intermediate-2, OR high-risk per the CMML Specific Prognostic Scoring System (CPSS) Molecular Model
* Atypical chronic myelocytic leukemia (aCML)
* MDS/MPN unclassified (MDS/MPN-U)
* Myeloproliferative neoplasm accelerated phase (MPN-AP)
* MPN-AP requires a previous diagnosis of polycythemia vera (PV), essential thrombocythemia (ET), or primary myelofibrosis (PMF) with intermediate-2 or high risk disease according to International Prostate Symptom Score (IPSS) as well as progression on or failure to respond to at least one line of therapy.
* Myelodysplastic syndrome/myeloproliferative neoplasm with ring sideroblasts and thrombocytosis (MDS/MPN-RS-T) or MDS/MPN with SF3B1 mutation and thrombocytosis (MDS/MPN-SF3B1-T).
* Not suitable for immediate myeloablative/intensive chemotherapy based on investigator assessment of age, comorbidities, local guidelines, institutional practice (any or all of these)
* PHASE Ib (RELAPSE \[R\]/ REFRACTORY \[R\]): Relapse/refractory patients who have received at least two cycles of disease directed therapy (prior therapies can include hypomethylating agents \[HMAs\], HMA combination therapies, and other disease directed therapies)
* PHASE II (NEWLY DIAGNOSED PHASE): Newly diagnosed patients without prior treatment, including intensive induction chemotherapy. However, previous treatment with hydroxyurea, ruxolitinib, and/or up to 2 cycles of HMAs (decitabine, azacitidine, oral decitabine \[INQOVI\]) is permitted
* Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3 × upper limit of normal (ULN)
* Total bilirubin ≤ 1.5 × ULN (except in the setting of isolated Gilbert syndrome)
* Estimated glomerular filtration rate (eGFR) ≥ 30 mL/min/1.73m\^2 (estimation based on Modification of Diet in Renal Disease \[MDRD\] formula, by local laboratory)
* Patient is able to communicate with the investigator and has the ability to comply with the requirements of the study procedures
* Women of childbearing potential and men, if not surgically sterilized, should use adequate contraception from 14 days prior to study entry and until 90 days after the last follow-up visit. Adequate contraception is defined as using hormonal contraceptives or an intrauterine device combined with at least 1 of the following forms of contraception: a diaphragm or cervical cap, or a condom
Exclusion Criteria:
* Diagnosis of acute myeloid leukemia (AML) including acute promyelocytic leukemia and extra-medullary AML based on WHO 2016 classification (Arber et al 2016)
* Patients who are candidates for myeloablative or intensive chemotherapy treatment or who do not provide consent for this treatment
* History of organ transplant or allogenic hematopoietic stem cell transplant
* Participants with prior malignancy, except:
* Participants with history of adequately treated malignancy for which no anticancer systemic therapy (namely chemotherapy, radiotherapy or surgery) is ongoing or required during the course of the study.
* Participants who are receiving adjuvant therapy such as hormone therapy are eligible. However, participants who developed therapy related neoplasms are not eligible
* Previous known allergy/sensitivity to components of axatilimab
* History of acute or chronic pancreatitis
* History of myositis
