Neoadjuvant Chemohormonal Therapy Followed by Salvage Surgery for High Risk PSA

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Life expectancy must be more than 10 years * Peripheral neuropathy: must be \</= grade 1 * A minimum PSA of 1 ng/ml if not on androgen deprivation therapy * Patients must have one of the following criteria to be eligible: * PSA recurrence with a doubling time of less than 9 months (calculated by at least 3 PSA values that were obtained at least 4 weeks apart) * Prostatic biopsy Gleason Grade of \>/= 8 at the time of initial biopsy prior to radiation therapy and as determined by either an outside pathology report or on review of slides by our institutional pathologist(s) * Clinical stage of \>/= T3 (defined as evidence of extracapsular or seminal vesicle extension on digital rectal examination or transrectal ultrasonography) either at the time of initial diagnosis or following radiotherapy * Prior radiation therapy of any type including external beam radiotherapy, brachytherapy, high dose radiotherapy, or proton therapy * Positive prostate biopsy documenting local recurrence following radiation therapy * Prior androgen deprivation therapy up to a total duration of 36 months is allowable. * Patients who are on LHRH analog therapy should continue such therapy provided that the patient does not have castration resistant prostate cancer (rising PSA in the presence of castrate levels of serum testosterone, ie \< 50 ng/dl). Androgen deprivation therapy other than LHRH analog should be discontinued 4 weeks prior to study enrollment. * All prostatic carcinoma variants except small cell carcinoma of the prostate will be allowed. * Patients must have no evidence of metastatic diseases on the bone scan and an abdominal/pelvic CT or MRI performed within 30 days of study enrollment. * All patients must be regarded as acceptable anesthetic risk for salvage surgery (salvage radical prostatectomy, salvage cystoprostatectomy, salvage total pelvic exenteration) and confirm their intention to undergo salvage surgery at the end of the neoadjuvant chemohormonal therapy. * Patients must have adequate bone marrow function defined as an absolute peripheral granulocyte count of \> 1,500/mm\^3 and platelet count of \> 100,000/mm\^3; adequate hepatic function defined with a total bilirubin of \< 1.5 mg/dl and aspartic transaminase/alanine transaminase (AST/ALT) \< 1.5 X the upper limits of normal (ULN); adequate renal function defined as serum creatinine clearance \> 60 ml/min (measured or calculated). * Men and women of childbearing potential must be willing to consent to using effective contraception while on treatment and for at least 3 months thereafter. * Patients must sign an informed consent indicating that they are aware of the investigational nature of this study, in keeping with the policies of the institution. * All patients must be evaluated in the Department of Genitourinary Oncology prior to signing informed consent. Exclusion Criteria: * Patients with small cell histology * Patients with clinical, radiological, or pathological evidence of bone, lymph node or visceral metastasis (liver or lung metastasis) * Castration resistant prostate cancer defined as rising PSA profile in setting of castrate levels of testosterone (serum testosterone \< 50 ng/dl) * Prior chemotherapy * Patients with severe or uncontrolled intercurrent infection * Patients with New York Heart Association (NYHA) Class III/IV congestive heart failure, unstable angina or history of myocardial infarction within the last 6 months * Contraindications to corticosteroids * Uncontrolled severe hypertension, persistently uncontrolled diabetes mellitus, oxygen dependent lung disease, chronic liver disease or HIV infection * Second malignancies (excluding non-melanoma skin cancer) unless disease-free for 3 years * Overt psychosis, mental disability or otherwise incompetent to give informed consent * Patients with a history of severe hypersensitivity reaction to Cabazitaxel® or other drugs formulated with polysorbate 80