I don’t necessarily like picking on series like Suicide Squad for their science, because the series do not have a focus on science at all.  Still when the science is there I don’t mind delving in to examine it a little more closely.  As always my scientific knowledge is restricted, but I will give it a shot anyway (spoilers as always).  

Physiology of the neck

It is a little unfair to pick on Suicide Squad for this specifically but I was going to run across this one way or the other eventually.  Starting in the 1980s and thanks largely to action movies there was a widespread belief that it was pretty easy to kill a person just by twisting their neck.  While this is indeed possible, the manner in which it is usually portrayed (that of a simple twisting of the neck) is not really how it is done, and so regardless of the pressure applied it is likely to give someone a bad case of whiplash as opposed to killing them.  Granted that Deadshot is a trained assassin but he we would require either superhuman strength or to do the right method in order to accomplish this, one of which he does not have, the other of which he is shown not doing. 

Verdict:  Bad Science 

Cyanide

The substance of choice for assassins everywhere, cyanide is a fairly effective killer, especially hydrogen cyanide, the gaseous version of the substance.  Without getting too much into detail, cyanide basically stops key energy transfers within the body (in major systems like nervous and arterial).   This is done by cyanide bonding with other key elements in the body which stops them from doing their tasks.  However, Diablo is shown here purging the drug from the body of the doctor.  Unlike some other poisons which cause certain amounts of cellular damage, there would not be a lot of damage done here necessarily as long as the person was still alive.  Getting them to medical help would be a good idea but not absolutely necessary if the substance was out of the blood stream. 

Verdict:  Bad Science