Interesting. I wonder if people have experimented with more humane slaughtering practices like giving the pigs a bunch of booze/opiates so they can have a big pig party, then slaughtering once they've had their fun and passed out. Seems like it could be much more humane. Give em a last hoorah.
Without looking it up, I would guess the go-to method usually would be anesthesia followed by an overdose of narcotics or a special euthanasia agent. It's just that a "Mini pig" of 70kg or more will require higher volumes of all of that compared to to a mouse or even a beagle. Of course, when using pharmaceuticals you can't use the meat.
In the EU it is also very dependent on what kind of medications the pigs received during the testing. Only if all of those have been explicitly allowed for meat production can the meat be used at all. Here in Germany the researchers would include the "what do I do afterwards with them" in the planning. So in some cases, like for experiments on feeding or maybe vaccines (if no infections are attempted) then they may actually plan to bring them into the food chain.
Nitrous oxide asphyxiation could be quite pleasant for the pig, and there would be little risk to anyone eating the tissue.
Euthanizing research pigs seems especially difficult. I'm really into butchery --- invested in a butcher in the area --- and would happily attend a slaughter. But the circumstances attending euthanizing research pigs are tricky; the pigs are all in a common area, and they're social animals and know something's up when you put one of them down. It messed with the boy.