Spontaneous Pachyderm Combustion.
Accidentally picked up from a lake by a firefighting helicopter and dropped onto a burning forest.
We had “drag racing accident” so how about “Drag Queen racing” accident? Those stiletto heels can be murder.
Laughing itself to death over the Monkey Haiku thread (collapsing on CBCD who finally stops writing monkey haikus).
Suffocation in Richard Gere?
Botched trunk amputation?
Shot by jealous husband. After all, what was the elephant doing in the refrigerator!
He was leaving footprints in the peanut butter. Come on, man, any five year old knows that! 
1920’s Style Death Ray.
As the victim of a robbery gone horribly wrong.
Swallowed by a hummingbird.
Didn’t that happen in The Little Prince ?
Taking a bullet for the Prime Minister.
Allergic reaction to peanuts
The knife thrower missed.
Eating pufferfish sushi (fugu)
or
In a storm at the top of Mt. Everest
Alzheimers.
So this elephant is on vacation (which means he’s indistinguishable from a mouse, but that’s a different story), he meets an attractive female elephant, they hit it off, they go back to her hotel room… The next thing he knows, the elephant wakes up in a bathtub full of ice. There’s a phone next to the bathtub, and a note on the wall that says “Call 911”. Of course, both of the elephant’s kidneys have been removed.
And he dies, because he can’t dial 911 on the phone with those hooves of his.
Land shark!
A pecular accident involving 3 Nuns and a collection of steam-powered origami animals.
Nastiest paper cuts you ever did see! 
Lorena Bobbitt and her knife.
Heart attack while watching Cubbies-Red Sox World Series*
*heart attack, yes. It’s the World Series that is least likely!
Hanta virus
Beams down wearing a red shirt.