Is neuter surgery safe for my 11-year-old dog with bloody urine?

I am sorry to hear about Prince. I am assuming your vet did a work-up including urinalysis and imaging (x-ray and ultrasound) to determine that a neuter is the recommended treatment for the hematuria. I am assuming that if they recommend a neuter it is because the issue is due to the prostate. If a work-up wasn't done to be certain this is the issue I would recommend one be done. We do have pets at this age go under anesthesia regularly, often for dental work. While anesthesia does pose risks for pets of any age, most do just fine, but it is recommended that they have pre-anesthetic bloodwork done to ensure that liver and kidney function are normal. I also recommend use of an IV catheter and fluids during anesthetic procedures and good anesthetic monitoring including pulse oximetry, blood pressure, and EKG in older patients. These tools help us keep the pet safe while under anesthesia. If your vet doesn't have the set up for good anesthetic monitoring, you can ask if they can refer you to a hospital that has this capability.