Some type of attack aim readjustment to the vital spots(neck?)
That is the idea of the "finish off" half of it, at least.
Attacks on vulnerable spots could be done at any time, but they are more likely to be used successfully against an incapacitated creature. I'm not sure if it's something that an adventurer could deliberately trigger or if it would be better to simply include it as a variation on a normal attack.
As for how vulnerabilities would be defined, I think it should be possible for the body raws to have information identifying the vulnerabilities a body part has to certain kinds of attacks. I'm not terribly knowledgeable of the DF raw format, so I'll leave coming up with a concrete example to others, but a creature's throat might be tagged to show that it is vulnerable to slitting. Perhaps armor raws could have the same sort of thing, so that eye slits and other potentially vulnerable features would be identified automatically.
This sort of system would allow a lot of vulnerabilities to be tagged on high level templates (all throats would have the same vulnerability to slitting, without Toady or a modder needing to tag it on each creature). It would also allow crazy creature types to have unusual vulnerabilities (e.g. blobs don't have throats, but their guts might spill out if their outer skin is punctured).
In case there's anyone who hasn't read The Hobbit, I'll put the last bit of my post in spoiler tags (and if you haven't, you should go buy a copy and read it).
A dragon like
Smaug might have a tag on his "upper body" part that says that there is a small spot where his otherwise impenetrable scales can be punctured. It's also interesting that the sharing of Bilbo's observations of the vulnerability that made Smaug's defeat by Bard the Bowman possible. Perhaps this kind of knowledge about megabeasts could be part of the legend system. Knowledge of more general sorts of weaknesses could probably be tied into the skill system (so that there'd be a specific skill involved in finding opportunities to slit throats). This is the sort of thing I was thinking of when I mentioned an "enemy knowledge" system.