Well, they can't just not report it at all, as much as that would be ideal.
*scratches head* Why not? Plenty of major news media groups don't report on stuff considerably more important than relatively isolated executions (See: US news media and basically anything having to do with south america, most anything to do with white slavery/general flesh trade, etc., so forth, so on.).
They report what's germane to the American public, but yeah. I had to argue against classmates in college who didn't think even the war in Afghanistan was worth covering despite their own people dying in it, and billions of our tax dollars being spent on it. That is the level of apathy the media has to work with, and so they go for the grisliest news that requires the least thinking on the part of their audience; someone getting their head cut off and a guy holding it up to camera as he shouts "Death to your country!" is not something most people will feel ambivalent about.
And it's not that they don't need to not report on it. But they need to not show the video, even an abridged version. The argument "well it's already out on the internet anyways" is the justification for compromising their own ethical standards. Gotta make dat money son. And once you're going to go that far....why not make it a HUGE banner ad, GO FOR THE ALL CAPS HEADLINE, and link every other story you've run where Americans have been beheaded. No one is learning much from the event except who died, who killed them and what the President is or isn't going to do about it.
This is why I prefer the print medium to this day. It's not immune to sensationalizing things, but I think it's much less apt to feed you junk news, just to get you emotionally riled up and trolling their website for an hour calling other people in the comments pieces of shit.