In Arrow in one of the last episodes of season three, Diggle and his wife travel with the Suicide Squad. They are escaping a building and Deadshot says he will hold off any bad guys that attempt to follow. They show him looking at a picture and then cut to an explosion. Is there any evidence that he was killed in the explosion or did he manage to escape?
It's always possible that he's still alive, but for the time being, in the Arrow universe, Deadshot is dead.
In-universe, all we know is that he volunteered to sacrifice himself to let Diggle and Layla escape, and was supposedly in the area of the explosion when it happened. We've not seen any hint of Deadshot since then, and everyone seems to believe he's dead.
Of course, it's a comic book show, so it's entirely possible he's not; people "seemingly" die all the time and return later. But in this case, there's a good out-of-universe reason to think he's dead: the Suicide Squad movie.
Unlike Marvel Studios, where the movies and TV shows all share a universe, in the DC world, the Arrowverse is a totally separate universe from the "DC Extended Universe", where Man of Steel, Dawn of Justice, and the other upcoming movies are set. In that universe, Deadshot is a member of the Suicide Squad, but a fundamentally different version than the Arrow one. (Also, he's played by Will Smith).
In order to avoid confusion among the viewers, the producers of Arrow have been told by Warner Bros that they can no longer use the Suicide Squad characters, like Harley Quinn and Deadshot, on the show. As long as this is the case, as far as Arrow is concerned, Deadshot is dead:
First, thanks for the kind words. I agree with you, our casting people — in Los Angeles and Vancouver — are the best. Unfortunately, Deadshot is off the table for the nonce.
-Marc Guggenheim src