Antiandrogen Therapy With or Without Axitinib Before Surgery in Treating Patients With Previously Untreated Prostate Cancer With Known or Suspected Lymph Node Metastasis

Inclusion Criteria: * Patients with adenocarcinoma of the prostate that in the opinion of the urologist could be resected after response to systemic therapy; ductal adenocarcinoma is permitted * Patients must be regarded as acceptable surgical risk for radical prostatectomy and confirm their intention to undergo radical prostatectomy at the end of the pre-surgical therapy * Eastern Cooperative Oncology Group (ECOG) performance status 2 or better * All patients must have thorough tumor staging and meet at least one of the following criteria: * Either lymph node biopsy or lymph node dissection demonstrating lymph node metastasis by prostate cancer * Non-bulky (\< 5 cm) regional pelvic or distant lymphadenopathy visualized on computed tomography (CT)/magnetic resonance imaging (MRI) scan; lymph node biopsy is required if \< 2.0 cm or in atypical distribution * Primary tumor Gleason score \>= 8 and serum prostate-specific antigen (PSA) concentration \>= 25 ng/mL, indicating high risk of occult lymph node metastases * Primary clinical tumor stage of T3 and Gleason score \>= 7, indicating high risk of occult lymph node metastases * Primary tumor stage T4, indicating high risk of occult lymph node metastases; patients in any of these groups and less than 3 sites of non-predominantly lytic bone metastasis will be still considered eligible for the trial; the 2010 American Joint Committee on Cancer (AJCC) staging system will be followed * Prior hormonal therapy (luteinizing hormone-releasing hormone \[LHRH\] agonist/antagonist with or without antiandrogen) up to 8 weeks is permitted * Absolute peripheral neutrophil count (ANC) of \>= 1,500/mm\^3 * Platelet count of \>= 100,000/mm\^3 * Total bilirubin of =\< 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x ULN * Serum creatinine =\< 1.5 x ULN or clearance \>= 60 mL/min (measured or calculated) * Urinary protein \< 2+ by urine dipstick (if \>= 2+, a 24-hour urine protein must show protein \< 2 g per 24 hours) * Patients or their partners must be surgically sterile or must agree to use effective contraception while receiving study treatment and for at least 3 months thereafter; the definition of effective contraception should be in agreement with local regulation and based on the judgment of the principal investigator or a designated associate * Patients must sign the current institutional review board (IRB) approved informed consent indicating that they are aware of the investigational nature of this study, in keeping with the policies of the institution, and willing and able to comply with scheduled visits, treatment plans, laboratory tests, and other study procedures * All patients must have a surgical and medical oncology consult prior to signing informed consent Exclusion Criteria: * Patients with biopsy-proven small cell or sarcomatoid histology * Patients with clinical or radiological evidence of bone (\>= 3 sites, or predominantly lytic if \< 3) or other extranodal metastasis * Patients who have had prior chemotherapy, experimental agents for prostate cancer, or patients receiving more than 8 weeks of prior hormone therapy will be excluded * Gastrointestinal abnormalities such as inability to take oral medication; requirement for intravenous alimentation; prior surgical procedures affecting absorption including total gastric resection; treatment for active peptic ulcer disease in the past 6 months; active gastrointestinal bleeding as evidenced by hematemesis, hematochezia or melena in the past 3 months without evidence of resolution documented by endoscopy or colonoscopy; malabsorption syndromes * Anticipated need for treatment with drugs that are known potent CYP3A4 inhibitors (i.e., verapamil, ketoconazole, miconazole, itraconazole, erythromycin, telithromycin, clarithromycin, indinavir, saquinavir, ritonavir, nelfinavir, lopinavir, atazanavir, amprenavir, fosamprenavir and delavirdine); grapefruit juice is also a CYP3A4 inhibitor * Anticipated need for treatment with drugs that are known CYP3A4 or CYP1A2 inducers (i.e. carbamazepine, dexamethasone, felbamate, omeprazole, phenobarbital, phenytoin, amobarbital, nevirapine, primidone, rifabutin, rifampin, and St. John's wort) * Patients with any infectious process that, in the opinion of the investigator, could worsen or its outcome be affected as a result of the investigational therapy * Patients with symptomatic congestive heart failure, unstable angina or myocardial infarction, coronary/peripheral artery bypass graft or repair, cerebrovascular accident or transient ischemic attack in the 12 months prior to randomization; or deep vein thrombosis or pulmonary embolism in the 6 months prior to randomization * Persistently uncontrolled diabetes mellitus, oxygen-dependent lung disease, chronic liver disease, or human immunodeficiency virus (HIV) infection * Inadequately controlled hypertension (defined as systolic blood pressure \> 140 mmHg and/or diastolic blood pressure \> 90 mmHg) despite antihypertensive medication, or prior history of hypertensive crisis or hypertensive encephalopathy * Evidence of bleeding diathesis or significant coagulopathy (in the absence of therapeutic anticoagulation) * Anticipation of need for major surgical procedure during the course of the study other than as outlined by the protocol * History of abdominal fistula or gastrointestinal perforation within 6 months prior to randomization * Serious, non-healing wound, active ulcer, or untreated bone fracture; any bone fractures must be healed * Known hypersensitivity to any component of axitinib or prior use of axitinib * Second malignancies (excluding non-melanoma skin cancer) unless treated with curative intent and disease-free for 3 years * Overt psychosis, mental disability, otherwise incompetent to give informed consent, or history of non-compliance * Planned participation in any other experimental drug study