ISIS has repeatedly been in the news for throwing gays off cliffs and buildings. I suspect they do this for two reasons.
First, it’s more convenient than stoning (the method prescribed by Islam). Going through the effort to tie someone up, throw them into a ditch and hurl rocks at them until they stop moving is quite gruesome and apt to turn the executioners’ against task unless they are bloodthirsty sadists (which many of them have proven themselves to be). Second, throwing someone off a building is an outlandish and theatrical act which wins ISIS a lot of press–which they view as a plus.
Whether or not the prophet would condone this deviation is at once an open question and an irrelevant one. As any decent person will tell you, we should not be throwing anyone off anything. Hulagu, Vlad the Impaler, Selim the Grim or Pat Robertson may find such a spectacle amusing, but it is prudent for people to distance themselves morally from such wicked and evil people.