Also an NFL (American football) term for the person whose job it is to approach players who are about to be cut (released, fired, etc) and tell them "The coach wants to see you, and bring your playbook" or something similar. The appearance of the Turk is the football equivalent to the Grim Reaper.

The Turk could be an actual person who actually does knock on doors and informs players of the bad news. It's also used in a symbolic sense, such as "The Turk will be coming tomorrow, when NFL teams must reduce their rosters to 53". Usually the term is associated with training camp, where teams gradually trim a large roster of potential players down to season size.

As for why the hatchetman is called "The Turk", the origins are hazy at best (I couldn't find anything conclusive). However, the most plausible explanation was found in an August 27, 2001 article by Scott Paulsen on Pittsburgh's 970 AM's website:

I imagine that the NFL started using "Turk" because of the Turkish soldiers of the 17th and 18th century and their long, curved scimitars. It’s a wonderful visual. Beware the Turk. He comes late at night, armed with a long, curved sword that he’ll used to cut you from the team!

Even if it's not the actual origin of the phrase, it sounds good...