Can a person live without a pancreas?  

Yes. You can be alive even after your entire pancreas has been removed. However, you would have very difficult to control diabetes. Also you would have problems with digestion and be required to take enzyme suppliments.
Pancreatectomy. Yes, but they would be very brittle diabetics because they would be missing all of he glucose homeostasis hormones that the pancreas secretes (insulin, glucagon, somatostatin) and their digestion would be poor because they would be missing the enzymes that the pancreas secretes that participate in digestion. There are oral enzyme preparations that help.
Yes. Many people have had to have the pancrease (pancrelipase) removed. This causes many health issues. First, there is diabetes due to this being the organ secreting insulin. This can be replaced. Next, is the absence of pancreatic digestive enzymes. Artifical pancreatic enzymes can be taken. Diarrhea is often the problem. None of this is optimum but sometimes the only alternative to keeping it.

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