Tivozanib Before Surgery in Treating Patients With Localized Kidney Cancer

Inclusion Criteria:

* Biopsy proven non-metastatic clear cell RCC, as per radiographic studies is T2 - T3a based on the American Joint Committee on Cancer (AJCC) 6th edition criteria
* Have an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2
* Hemoglobin \>= 10 gm/dL
* Absolute neutrophil count (ANC) \>= 1.5 X 10\^9/L
* Platelets \>= 100 X 10\^9/L
* Total bilirubin \< 1.5 X upper limit of normal (ULN)
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \< 2.5 X ULN
* International normalization ratio (INR) \< 1.5
* Activated partial thromboplastin time (aPTT) \< 1.2 X ULN
* Serum creatinine \< 1.5 mg/dL or if \>= 1.5 mg/dL: calculated creatinine clearance (CrCL) \> 30 mL/min based on Cockroft-Gault formula
* Must have the ability to swallow and retain oral medication
* Patients of childbearing potential must agree to use acceptable contraceptive methods (e.g., double barrier) during treatment
* Patient or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure

Exclusion Criteria:

* Pregnant or nursing female patients
* Unwilling or unable to follow protocol requirements
* Any condition which in the Investigator's opinion deems the patient an unsuitable candidate to receive tivozanib (solitary kidney, multiple tumors in the same or contralateral kidney)
* Not a candidate for surgery
* Received an investigational agent within 30 days prior to enrollment
* Non-clear cell or sarcomatoid histology
* Patients with metastatic disease at presentation
* Prior therapy with tyrosine kinase inhibitor for RCC
* A second primary malignancy (except squamous and basal cell carcinoma of skin) in the past 3 years
* Active or chronic infections
* Significant cardiovascular disease, including:

  * Clinically symptomatic left ventricular failure
  * Uncontrolled hypertension: systolic blood pressure of \> 150 mmHg or diastolic blood pressure of \> 100 mmHg documented on 2 consecutive measurements taken at least 24 hours apart
  * Myocardial infarction, severe angina, or unstable angina within 6 months prior to administration of first dose of tivozanib
  * History of serious ventricular arrhythmia (i.e., ventricular tachycardia or ventricular fibrillation)
  * Cardiac arrhythmias requiring anti-arrhythmic medications (except for atrial fibrillation that is well controlled with anti-arrhythmic medication)
  * Coronary or peripheral artery bypass graft within 6 months of screening
* History of coronary artery disease or peripheral arterial disease
* History of stroke or carotid endarterectomy
* Patients who are taking cytochrome P450 system (CYP)3A4 inducers are excluded; patients taking CYP3A4 inducers that can be safely replaced with another agent may be enrolled after a 5 day washout period