Mogamulizumab and Extracorporeal Photopheresis for the Treatment of Sezary Syndrome or Mycosis Fungoides

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Histopathologic diagnosis of primary cutaneous T-cell non-Hodgkin lymphoma (CTCL) (mycosis fungoides \[MF\] or Sezary syndrome \[SS\]), confirmed by skin biopsy, or lymph node, or blood assessment, of current disease * CTCL stage 3A-4A2 disease at study entry according to International Society of Cutaneous Lymphoma (ISCL)/European Organization for Research and Treatment of Cancer (EORTC) * Newly diagnosed or =\< 3 different lines of systemic therapy * Systemic therapy includes oral retinoids, interferon, pralatrexate, methotrexate, vorinostat, romidepsin, single or multi-agent chemotherapy or other oral, IV or subcutaneous treatments used to treat systemic disease * A line of therapy is defined as any therapy or group of therapies that was started or changed for lack of response, disease progression, or intolerance * Prior cytotoxic chemotherapy excluding low dose methotrexate * A minimum washout period of 4 weeks after previous CTCL therapy is recommended prior to the first dose of combination therapy * Willing and able to comply with all aspects of the protocol * Provide voluntary written informed consent prior to any study specific screening procedures * Absolute neutrophil count (ANC) \>= 500/mcL (within 16 days of cycle 1 day 1) * Platelets \>= 50,000/mcL (within 16 days of cycle 1 day 1) * Total bilirubin =\< 3 institutional upper limit of normal (ULN) (within 16 days of cycle 1 day 1) * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 5 institutional upper limit of normal (ULN) (within 16 days of cycle 1 day 1) * Not dialysis dependent, creatinine clearance \>= 30 mL/min (within 16 days of cycle 1 day 1) * Female of child-bearing potential (FCBP) must have a negative serum or urine pregnancy test prior to starting therapy: documented by negative beta-human chorionic gonadotropin \[beta-hCG\] test with a minimum sensitivity of 25 IU/L or equivalent units of beta-hCG. A separate baseline assessment is required if a negative screening pregnancy test was obtained more than 72 hours before the first dose of study drug * FCBP and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation and 30 Days after completion. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 30 days after completion of study drug administration. A female of childbearing potential (FCBP) is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months Exclusion Criteria: * Visceral involvement except for CTCL involvement of the bone marrow * Bulky lymphadenopathy (\> 5 cm), or pathologically N3 lymph node involvement * Total skin electron beam therapy within 6 months prior to registration * Prior allogeneic transplantation * Prior mogamulizumab therapy within 6 months of registration or progression or intolerance of mogamulizumab * Patients with 2 or less doses of prior mogamulizumab prior to registration will be eligible regardless of date mogamulizumab was received * Patients who received mogamulizumab pre-study enrollment would restart day 1 dosing per protocol * Prior ECP \> 2 months in duration within 3 months of registration * Patients with ECP treatment prior to registration will be eligible regardless of date ECP was received (as long as it was not \> 2 months in duration within the 3 months immediately prior to registration), as long as they have measurable disease at the time of enrollment * Use of topical steroids within 14 days of day 1 of initial therapy is not allowed, with the following exception: * Topical steroids or systemic low dose steroids (=\< 10 mg/day prednisone) are allowed in subjects with erythroderma who have been on corticosteroids for a prolonged period of time and where discontinuation may lead to rebound flare in disease. The concomitant steroid medication is allowed as long as the type of steroid, route of administration, and steroid dose remain the same as what the subject had been receiving for a prolonged period of time * Severe or uncontrolled autoimmune condition * Active, life threatening malignancy (except for CTCL, definitively treated basal or squamous cell carcinoma of the skin, and carcinoma in-situ of the cervix, or other localized malignancies treated with curative intent with surgery or radiation alone) within the past 12 months * Serious intercurrent illness * Known significant cardiac disease requiring ongoing treatment, including congestive heart failure (CHF), severe coronary artery disease (CAD), cardiomyopathy, uncontrolled cardiac arrhythmia, unstable angina pectoris, or myocardial infarction (MI) (within 6 months of study enrollment) * Major surgery within 2 weeks of study enrollment * Significant or uncontrolled infections requiring systemic anti-infective therapy * Patients with human immunodeficiency virus (HIV) infection are eligible. Patients with HIV infection must meet the following: No evidence of co-infection with hepatitis B or C; CD4+ count \> 400/mm; no evidence of resistant strains of HIV; on anti-HIV therapy with an HIV viral load \< 50 copies HIV RNA/mL. Patients with HIV must have ongoing follow-up with an infectious disease specialist and must have been evaluated within 90 days of cycle 1 day 1 * Patients with a history of hepatitis C are eligible as long as the hepatitis C has been treated and cleared and they have no evidence of hepatic dysfunction related to hepatitis C. Patients must have been seen by a hepatologist within 6 months of cycle 1 day 1 * Patients who test positive for hepatitis B core antibody may enroll on the study as long as they test negative for both hepatitis B surface antigen and hepatitis B deoxyribonucleic acid (DNA), and if they have no evidence of hepatic dysfunction that is felt to be related to hepatitis B * Patients may not have an auto-immune disease requiring systemic immunosuppression, biologic therapy, and/or steroid use (\>= 10 mg daily of prednisone or equivalent) * Patients will not be excluded based on CCR4 expression * Females who are pregnant (positive urine test) or breastfeeding