Axitinib Before Surgery in Treating Patients With High-Risk Prostate Cancer

Inclusion Criteria: * Histologically confirmed diagnosis of prostate cancer * High-risk prostate cancer as defined by 1 of the 3 following criteria: * Baseline prostate specific antigen (PSA) \> 20 * Clinical stage \>= T3a and * Gleason score 8-9 * Subjects must be appropriate candidates for prostatectomy and pelvic lymph node dissection, as deemed by multidisciplinary tumor team; subjects must provide informed consent to these procedures prior to initiating study treatment * Subjects must provide written informed consent prior to performance of study-specific procedures or assessments, and must be willing to comply with treatment and follow-up; procedures conducted as part of the subject's routine clinical management (e.g., blood count, imaging study) and obtained prior to signing of informed consent may be utilized for screening or baseline purposes provided these procedures are conducted as specified in the protocol * Absolute neutrophil count (ANC) \>= 1500 cells/mm\^3 * Platelets \>= 100,000 cells/mm\^3 * Hemoglobin \>= 9.0 g/dL * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 X upper limit of normal (ULN) * Total bilirubin =\< 1.5 X ULN * Serum creatinine =\< 1.5 X ULN or calculated creatinine clearance \>= 60 mL/min * Urinary protein \< 2+ by urine analysis (UA); if UA is \>= 2+ for protein then a 24-hour urine collection can be done and the patient may enter only if urinary protein is \< 2 g per 24 hours * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Life expectancy of \>= 12 weeks * No prior systemic therapy for prostate cancer * No evidence of preexisting uncontrolled hypertension as documented by 2 consecutive blood pressure readings taken within 1 hour; the baseline systolic blood pressure readings must be =\< 140 mm mercury (Hg), and the baseline diastolic blood pressure readings must be =\< 90 mm Hg; patients whose hypertension is controlled by antihypertensive therapies are eligible * Within 2 weeks of consent (and prior to initiating systemic therapy with axitinib if randomized to that arm), patients should visit with a radiation oncologist to discuss the option of radiation therapy (potentially with concomitant androgen deprivation therapy) for high-risk disease; if the patient has met with a radiation oncologist within 3 months of study enrollment to discuss the possibility of radiation therapy for localized prostate cancer, then this will suffice; patients do not have the right to refuse consultation; if this is the case, it must be documented by the treating physician in the medical record * Signed and dated informed consent document indicating that the patient (or legally acceptable representative) has been informed of all pertinent aspects of the trial prior to enrollment Exclusion Criteria: * Prior systemic therapy for prostate cancer (including by not limited to endocrine therapy; i.e., LHRH analogues, antiandrogens, etc.) * Evidence of metastatic disease * Prior radiation therapy for prostate cancer * Known history of allergic reactions to axitinib or other VEGF-TKIs * Presence of serious or uncontrollable infection * Major surgery \<4 weeks of starting the study treatment * Gastrointestinal abnormalities including: * 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, unrelated to cancer, as evidenced by hematemesis, hematochezia or melena in the past 3 months without evidence of resolution documented by endoscopy or colonoscopy * Malabsorption syndromes * Current use or anticipated need for treatment with drugs that are known potent cytochrome P450 3A4 (CYP3A4) inhibitors (ie, grapefruit juice, verapamil, ketoconazole, miconazole, itraconazole, erythromycin, telithromycin, clarithromycin, indinavir, saquinavir, ritonavir, nelfinavir, lopinavir, atazanavir, amprenavir, fosamprenavir and delavirdine) * Current use or anticipated need for treatment with drugs that are known CYP3A4 or cytochrome P450 1A2 (CYP1A2) inducers (ie, carbamazepine, dexamethasone, felbamate, omeprazole, phenobarbital, phenytoin, amobarbital, nevirapine, primidone, rifabutin, rifampin, and St. John's wort) * Requirement of anticoagulant therapy with oral vitamin K antagonists; therapeutic use of low molecular weight heparin is allowed * Active seizure disorder * A serious uncontrolled medical disorder or active infection that would impair their ability to receive study treatment * Any of the following within the 12 months prior to study drug administration: myocardial infarction, uncontrolled angina, coronary/peripheral artery bypass graft, symptomatic congestive heart failure, cerebrovascular accident or transient ischemic attack and 6 months for deep vein thrombosis or pulmonary embolism * Known human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS)-related illness * History of a malignancy (other than prostate cancer) except those treated with curative intent for skin cancer (other than melanoma), in situ breast or in situ cervical cancer, or those treated with curative intent for any other cancer with no evidence of disease for 2 years * Dementia or significant altered mental status that would prohibit the understanding or rendering of informed consent and compliance with the requirements of this protocol * Other severe acute or chronic medical or psychiatric condition, or laboratory abnormality that may increase the risk associated with study participation or study drug administration, or may interfere with the interpretation of study results, and in the judgment of the investigator would make the patient inappropriate for entry into this study