'American Hoggers' -- Under Attack for Ultra-Violent Pig Slaughter

The gun-toting family on A&E's new reality show "American Hoggers" are under fire from an animal rights group for the gruesome way the pigs are "tied up and shot" on the show ... TMZ has learned.

In case you haven't seen it -- "American Hoggers" follows Jerry "Hog Boss" Campbell ... and his family as they hunt and kill feral pigs ... armed with hunting dogs and guns. It's pretty graphic ... even for A&E.

The show just premiered this week -- and it didn't take long for PETA to take notice. In fact, the animal rights org. has just released a statement saying, "the Campbells' show promotes cruel animal-control measures and gross mistreatment of wildlife."

PETA claims it acknowledges that feral pigs can be problematic in parts of Texas, but the group says, "If property owners insist on lethal control, then feral hogs should be cage-trapped and afforded a quick, painless death."

We reached out to A&E for comment, and so far haven't received a response.

** WARNING -- the clip is very graphic **