If you are referring to the movie's plot or a specific scene, "piece" often refers to the the killer removes from victims.
Users on the official YTS site often leave comments on the "depth" of a movie's plot or the quality of the "piece" (the film itself). A "deep piece" might simply be a user's way of calling the movie a "deep" or "profound" work of horror.
The phrase "deep piece" isn't a standard cinematic or technical term associated with the movie Jigsaw or the YIFY (YTS) release group. However, based on how these terms are commonly used in online circles and torrent communities, here are the likely interpretations: 1. File or Release Information