Gemtuzumab Ozogamicin in Treating Patients With Relapsed or Refractory Acute Myeloid Leukemia or Acute Promyelocytic Leukemia

Inclusion Criteria: * Diagnosis of relapsed or refractory AML and not candidate for standard consolidation treatment after daunorubicin and cytosine arabinoside OR diagnosis of APL relapsed after tretinoin (ATRA) and arsenic trioxide therapy or APL with persisting or rising blasts, and no other comparable or satisfactory alternative therapy available (including patients not eligible for, or who have access to, investigational therapies via a clinical trial) * Patients must have an initial diagnosis of AML, biphenotypic acute leukemia, or APL * Patients must have cluster of differentiation (CD)33 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 glutamate pyruvate transaminase \[SGPT\]) =\< 2 x institutional upper limit of normal * It is deemed ethical to provide an experimental drug (e.g., Mylotarg) that is associated with hepatotoxicity (veno-occlusive disease \[VOD\]) and myelosuppression * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to receiving Mylotarg and for the duration of treatment; should a woman become pregnant or suspect she is pregnant while receiving treatment with Mylotarg, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written Institutional Review Board (IRB)-approved informed consent document Exclusion Criteria: * Patients may not currently be receiving any other investigational agents for leukemia * Patients with known untreated hepatitis C * Uncontrolled intercurrent illness including, but not limited to active liver disease, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with Mylotarg * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated * Patients with a known hypersensitivity to gemtuzumab ozogamicin or its parts: recombinant humanized anti-CD33 monoclonal (hP67.6) antibody, calicheamicin derivatives or other ingredients