This randomized pilot clinical trial studies sipuleucel-T with or without deoxyribonucleic acid (DNA) vaccine therapy in treating patients with prostate cancer that has not responded to previous treatment with hormones and has spread to other places in the body. Vaccines may help the body build an effective immune response to kill tumor cells. It is not yet known whether giving sipuleucel-T vaccine works better with or without DNA vaccine therapy in treating prostate cancer.