When do audiences approve of graphic depictions of animated violence?

The ethics of depicting violence in film and animation has always fascinated me.  Do audiences ever approve the kill off of characters?  Even if audiences will approve the death of a character - should you do it?  Does the manner of death matter?  

The answer to the latter is yes, it matters, and there are specific ways to go about ending characters lives and each method will evoke particular emotions from your viewers.  Once you learn these you'll be able to determine which method you use.

For this example, let's say you feel your story won't be complete without a scene depicting a graphically violence act, but you want to make sure that the majority of your audience won't be too offended by it.  Well, that requires very special characters.  To use extreme examples, lets look at two shows that have actually based their franchises on depicting character types that generally receive audience approval for being killed off.  These shows are Superjail and Happy Tree Friends.

We're going to start with Superjail. Even though the violence depicted is extreme and unconventional the creators have followed a very conventional narrative tactic to justify the violence to the audience.  The majority of the characters killed are all inmates, and thus criminals, and so we as a society tacitly approve their deaths.  You can see this narrative tactic used all the time, especially by Disney.  When "evil" characters die it's a "good" thing.  Disney's version is like lethal injection while Superjail's version is like nothing I've ever seen before.  The key to having the audiences approve these deaths is by doing little to no character building aside from assigning the role of inmate - otherwise you'll end up eliciting reactions similar to the ones caused by the electrocution scene from The Green Mile. 

Side Note: The Green Mile is actually the perfect example of a writer, Stephen King, turning this conventional 'it's okay to kill inmates because they're criminals' narrative on it's head.  If you haven't seen the Green Mile yet, you should, it's a fantastic film.  I cried at the end.

Now let's move on to Happy Tree Friends where the creators have made the sweetest characters known to man and then had them die the most horrible deaths imaginable.  This of course taps into our inner dark side.  We've all been in situations where someone is just far too cheerful when we're having a gloomy day and it would likely raise our spirits if we fantasized about them falling down a well. Happy Tree friends is the creative expression of just such a feeling - and in their case the well would include spikes, a motion activated flamethrower, and a portal to the sun's surface.

Ok, so those are two ways to get tacit audience approval for graphic displays of violence in your animations.  Depict it happening to either the happiest or the worst members of a society.  Going after the average character always seems to hit a little too close to home for most viewers, but sometimes you can get away with it by spending a little time enhancing their happiness/evil characteristics during the episode that things go horrible awry for them.