Filgrastim, Cladribine, Cytarabine, and Mitoxantrone Hydrochloride in Treating Patients With Newly Diagnosed or Relapsed/Refractory Acute Myeloid Leukemia or High-Risk Myelodysplastic Syndromes

Inclusion Criteria: * For patients with newly diagnosed disease: diagnosis of "high-risk" myelodysplastic syndrome (MDS) (\>= 10% blasts) or AML other than acute promyelocytic leukemia (APL) with t(15;17)(q22;q12) or variants according to the 2008 World Health Organization (WHO) classification; for patients with relapsed/refractory disease: prior diagnosis of "high-risk" MDS or non-APL AML, with relapsed/refractory disease according to standard criteria requiring first or subsequent salvage therapy; patients with biphenotypic AML are eligible * Outside diagnostic material is acceptable as long as peripheral blood and/or bone marrow slides are reviewed at the study institution; flow cytometric analysis of peripheral blood and/or bone marrow should be performed according to institutional practice guidelines * For patients with relapsed/refractory disease: patients with prior autologous or allogeneic hematopoietic cell transplantation (HCT) for MDS/AML are eligible if relapse occurs provided symptoms of graft-versus host disease are well controlled with stable use of immunosuppressive agents * Treatment-related mortality (TRM) score =\< 6.9 as calculated with simplified model * The use of hydroxyurea prior to study registration is allowed; patients with symptoms/signs of hyperleukocytosis or white blood cell (WBC) \> 100,000/uL can be treated with leukapheresis or may receive up to 2 doses of cytarabine (up to 500 mg/m\^2/dose) prior to enrollment * For patients with relapsed/refractory disease: patients may have previously received chemotherapy with a mitoxantrone- or cladribine-based regimen for MDS or AML; if that patient has received G-CLAM before and has been sensitive to this regimen, eligibility will be determined on a case-by-case basis by the study principal investigator (PI) * Should be off any active systemic therapy for AML with the exception of hydroxyurea for at least 14 days prior to study registration unless patient has rapidly progressive disease, and all grade 2-4 non-hematologic toxicities should have resolved * Bilirubin =\< 2.5 x institutional upper limit of normal (IULN) unless elevation is thought to be due to hepatic infiltration by AML, Gilbert's syndrome, or hemolysis (assessed within 14 days prior to study day 0) * Serum creatinine =\< 2.0 mg/dL (assessed within 14 days prior to study day 0) * Left ventricular ejection fraction \>= 45%, assessed within 3 months prior to study day 0, e.g. by multi gated acquisition scan (MUGA) scan or echocardiography, or other appropriate diagnostic modality and no clinical evidence of congestive heart failure; if the patient had anthracycline-based therapy since the most recent cardiac assessment, cardiac evaluation should be repeated if there is clinical or radiographic suspicion of cardiac dysfunction, or if the previous cardiac assessment was abnormal * Women of childbearing potential and men must agree to use adequate contraception * Provide written informed consent Exclusion Criteria: * Myeloid blast crisis of chronic myeloid leukemia (CML), unless patient is not considered candidate for tyrosine kinase inhibitor treatment * Concomitant illness associated with a likely survival of \< 1 year * Active systemic fungal, bacterial, viral, or other infection, unless disease is under treatment with anti-microbials and/or controlled or stable (e.g. if specific, effective therapy is not available/feasible or desired \[e.g. chronic viral hepatitis, human immunodeficiency virus (HIV)\]); patient needs to be clinically stable as defined as being afebrile and hemodynamically stable for 24 hours; patients with fever thought to be likely secondary to leukemia are eligible * Known hypersensitivity to any study drug * Pregnancy or lactation * Treatment with any other investigational agent