Set the multi-function pressure cooker to the brown function or heat large sauté pan on the stovetop over medium-high heat. Add the olive oil and sear the pork pieces on all sides until lightly browned all over. Remove the pork and set aside. Add the diced onion to the cooker or pan and sauté for a few minutes, until browned. Deglaze the cooker or pan by pouring in the beer and scraping up any browned bits on the bottom of the cooker or pan. Simmer the beer for 1 minute, then add the beef stock, brown sugar and apple cider vinegar. Simmer everything for a few more minutes.
Return the browned pork to the pressure cooker with the liquid or load the pork into the slow cooker and transfer the onions and liquid from the pan to the pressure cooker. Lock the lid in place. Pressure cook on HIGH for 65 minutes.
Let the pressure drop NATURALLY for at least 15 minutes and then carefully open the lid.
Remove the pork from the cooker and shred it on a cutting board with two forks. Set it aside. Pour the braising liquid from the pressure cooker into a fat separator and let the fat rise to the surface. Add 1 cup of the liquid to the mango BBQ sauce and reserve the rest.
Return the shredded pork to the cooker and add the mango BBQ sauce, stirring to combine well, and return the cooker to the brown setting to bring the mixture to a simmer, stirring regularly so that it doesn't stick or burn to the bottom. Turn the cooker off and let the meat cool to an edible temperature. If necessary, adjust the meat mixture to your desired consistency by adding more of the reserved braising liquid to the pork.