Filgrastim, Cladribine, Cytarabine, and Mitoxantrone With Sorafenib in Treating Patients With Newly-Diagnosed, Acute Myeloid Leukemia or High-Risk Myelodysplastic Syndrome

Inclusion Criteria:

* Age 18-60 years, inclusive
* Newly diagnosed disease with either a diagnosis of "high-risk" MDS (\>= 10% blasts in marrow or blood), high-risk myeloproliferative neoplasm (MPN; \>= 10% blasts in blood or bone marrow), 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. Patients with biphenotypic AML are eligible; such "high-risk" MDS or MPN have natural history much closer to AML than to lower risk MDS or MPN and have responded similarly to "AML-type" therapy.
* Outside diagnostic material is acceptable as long as peripheral blood and/or bone marrow slides are reviewed at the study institution by appropriate clinical staff. Flow cytometric analysis of peripheral blood and/or bone marrow should be performed according to institutional practice guidelines.
* Treatment-related mortality (TRM) score =\< 13.1 as calculated with simplified model
* The use of hydroxyurea prior to study registration is allowed. Patients with symptoms/signs of hyperleukocytosis, white blood cell (WBC) \> 100,000/uL, or acute symptoms can be treated with leukapheresis or may receive up to 2 doses of cytarabine (up to 500 mg/m\^2/dose) prior to study day 0 enrollment
* Bilirubin =\< 2 times institutional upper limit of normal unless elevation is thought to be due to hepatic infiltration by AML, Gilbert's syndrome, or hemolysis (assessed within 10 days prior to study day 0)
* Serum creatinine =\< 2.0 mg/dL (assessed within 10 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
* Women of childbearing potential and men must agree to use adequate contraception beginning at the signing of the consent until at least 3 months after the last dose of study drug
* Provide written informed consent (or legal representative)

Exclusion Criteria:

* Myeloid blast crisis of chronic myeloid leukemia (CML), unless patient is not considered candidate for CML-directed tyrosine kinase inhibitor treatment (excluding sorafenib)
* 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 24-48 hours prior to study day 0, unless fever is thought to be secondary to the underlying hematologic disease.
* Active or clinically significant (or symptomatic) cardiac disease, including active coronary artery disease, cardiac arrhythmias requiring anti-arrhythmic therapy other than beta blockers or digoxin within the last 3 months, unstable angina (anginal symptoms at rest), new-onset angina within 3 months before randomization, or myocardial infarction within 6 months before study day 0
* Previous receipt of azacitidine, decitabine, anthracyclines, cytarabine, or other nucleoside analogues for treatment of AML or MPN/MDS other than as noted for cytarabine
* Pregnancy or lactation
* Concurrent treatment with any other investigational agent that has anti-leukemia activity or another drug with anti-AML-activity