Inclusion Criteria:  The patient is >= 18 years old  Diagnosis of myelodysplastic/myeloproliferative neoplasm (MDS/MPN) subtype chronic myelomonocytic leukemia (CMML) according to World Health Organization (WHO) and:  Phase 1 dose escalation portion: CMML-1 or CMML-2 by WHO and no response after 6 cycles of azacitidine, decitabine, guadecitabine or ASTX727 (decitabine-cedazuridine) or relapse or progression after any number of cycles  Phase 2 dose expansion portion:  Relapsed cohort (Cohort A): CMML-1 or CMML-2 by WHO and no response after 6 cycles of azacitidine, decitabine, guadecitabine or ASTX727 (decitabine-cedazuridine) or relapse or progression after any number of cycles Hypomethylating agents (HMA) naive cohort (Cohort B): CMML-1 or CMML-2 and intermediate-2 or high-risk International Prognostic Scoring System (IPSS) The patient has an Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0-2 Left ventricular ejection fraction (LVEF) >= 50% as measured by multigated acquisition scan or 2-dimensional (2-D) echocardiogram (ECHO) within 28 days prior to start of therapy and no clinically significant abnormalities on a 12-lead electrocardiogram (ECG) Serum creatinine =< 1.5 mg/dL (or =< 114 umol/L) Serum albumin >= 3.2 g/dL (or >= 32 g/L) in the absence of receipt of (IV) albumin within the previous 72 hours Total Bilirubin =< 1.5 mg/dL (or =< 26 umol/L) Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2.5 times the upper limit of normal (ULN) Creatine kinase (CK) =< 2.5 times the ULN If a woman of child bearing potential (WOCBP), the patient has a negative serum or urine pregnancy test within 1 week prior to tagraxofusp treatment (intervals shorter than 1 week are acceptable, if required by institutional guidelines) The patient or legally authorized representative has signed informed consent prior to initiation of any study-specific procedures or treatment The patient is able to adhere to the study visit schedule and other protocol requirements, including follow-up for response assessments The patient (either male or female) agrees to use acceptable contraceptive methods for the duration of time in the study, and to continue to use acceptable contraceptive methods for 2 months after the last tagraxofusp infusion Patient has an absolute neutrophil count (ANC) >= 0.5 x 10^9/L  Exclusion Criteria:  Patient has persistent clinically significant toxicities grade >= 2 from previous chemotherapy not readily controlled by supportive measures (excluding alopecia, nausea, and fatigue) Patient has received treatment with chemotherapy, wide-field radiation, or biologic therapy within 14 days of study entry Patient has received treatment with another investigational agent within 14 days of study entry or concurrent treatment with another investigational agent Patient has previously received treatment with tagraxofusp or has a known hypersensitivity to any components of the drug product Patient has an active malignancy and/or cancer history (excluding myeloproliferative disorders and concomitant myeloid malignancies as specified in the inclusion criteria) that is requiring active therapy. Patients with the following neoplastic diagnoses are eligible: non-melanoma skin cancer, carcinoma in situ (including superficial bladder cancer), cervical intraepithelial neoplasia, or organ- confined prostate cancer with no evidence of progressive disease Patient has clinically significant cardiovascular disease (e.g., uncontrolled or any New York Heart Association class 3 or 4 congestive heart failure, uncontrolled angina, history of myocardial infarction, unstable angina, or stroke within 6 months prior to study entry, uncontrolled hypertension or clinically significant arrhythmias not controlled by medication) Patient has uncontrolled, clinically significant pulmonary disease (e.g., chronic obstructive pulmonary disease, pulmonary hypertension) that, in the Investigator's opinion, would put the patient at significant risk for pulmonary complications during the study Patient has known active or suspected disease involvement of the central nervous system (CNS). If suspected due to clinical findings, CNS disease should be ruled out with relevant imaging and/or examination of cerebrospinal fluid Patient is receiving immunosuppressive therapy, with the exception of corticosteroids and tacrolimus, for treatment or prophylaxis of graft- versus-host disease (GVHD). If the patient has been on immunosuppressive treatment or prophylaxis for GVHD, the treatment(s) must have been discontinued at least 14 days prior to study drug and there must be no evidence of grade >= 2 GVHD Patient has uncontrolled intercurrent illness including, but not limited to, uncontrolled infection, disseminated intravascular coagulation, or psychiatric illness that would limit compliance with study requirements Patient is pregnant or breast feeding Patient has known human immunodeficiency virus (HIV) Patient has evidence of active or chronic hepatitis B or hepatitis C infection Patient is oxygen-dependent Patient has any medical condition that in the Investigator's opinion place the patient at an unacceptably high risk for toxicities