Gemtuzumab Ozogamicin in Treating Patients With Acute Myeloid Leukemia

Inclusion Criteria: * Patients must have confirmed relapsed or refractory acute myeloid leukemia and not a candidate for standard induction treatment after daunorubicin and cytosine arabinoside OR acute promyelocytic leukemia relapsed after all-trans retinoic acid (ATRA) or Arsenic trioxide therapy * Patients must have an initial diagnosis of acute myeloid leukemia or biphenotypic acute leukemia * Patients must have CD33 positivity of \>= 30% * Eastern Cooperative Oncology Group (ECOG) performance status =\< 3 * Karnofsky \> 60% * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase \[SGPT\]) =\< 2 X institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 30 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * The effects of Mylotarg on the developing human fetus are unknown; for this reason and because Mylotarg class agents 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; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients may not be receiving any other investigational agents for leukemia * Patients with known untreated Hepatitis C because veno-occlusive disease and liver enzyme abnormalities have been associated with Mylotarg * Uncontrolled intercurrent illness including, but not limited to active liver disease, ongoing or active sepsis requiring vasopressors or mechanical ventilation, symptomatic congestive heart failure, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because Mylotarg is a Class D agent 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 Mylotarg, breastfeeding should be discontinued if the mother is treated with Mylotarg * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with Mylotarg; in addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated * Congestive Heart Failure (CHF) with an ejection fraction \< 30% * Glomerular filtration rate (GFR) \< 30ml/min * Active central nervous system (CNS) involvement of leukemia * Philadelphia chromosome + acute lymphoblastic leukemia (ALL) * Prior hematopoietic transplant in last 3 months