A few years back there was a very funny British TV comedy series, set in a TV news organisation. It was called "Drop the Dead Donkey", and the reason for this rather odd title was never explained. I assumed that it was meant to refer to some newsroom jargon for a "breaking news" item coming in and superseding a rather trivial item concerning a deceased pet donkey, or something like that.
My understanding is that the title was inspired by a long running story in one of the British tabloids. Considerable coverage had been given to the practise of pushing a donkey to its doom from a church or bell tower as part of a Spanish festival. To the best of my recollection, considerable efforts were made by the readership of the newspaper concerned, to rescue the donkey next in line for a violent demise. As far as the title of the series is concerned, presumably a more pressing story had broken. It is rather a long time ago, and my memory is perhaps not what it once was, but I think that my account will stand scrutiny. Time does not permit searching around the web for a more definitive explanation.