According to NFL media insiders Ian Rapoport and Mike Garafolo, Mays was cut because of another failed drug test that could now cost him eight or more games in 2016.
If S Taylor Mays is ready to play after his latest suspension (for at least 8 games total), Cincy hasn't ruled out bringing him back— Ian Rapoport (@RapSheet) July 25, 2016
As Rapoport alluded to, it's possible the Bengals look to bring Mays back later in the year if they need some emergency depth at linebacker and/or safety, but we won't see him on an NFL field for at least the first two months of the season, it appears.
Mays has played 50 games for the Bengals, including an eight-game stretch in 2013 where he played a linebacker/safety hybrid role. An injury ended his season midway through 2013, and after playing sparingly in 2014, he left to sign with the Vikings in 2015, though he was cut before the regular season began.
Mays did spend last season with the Raiders and appeared in 14 games. He even made five starts opposite Charles Woodson at safety and finished with a respectable 64.6 Pro Football Focus grade. As he became a free agent this offseason, Mays could've seen decent interest on the open market, but a four-game suspension to start the 2016 season dissuaded teams away from him.
That suspension is for violating the NFL's policy on substances of abuse, as is his latest offense. At this point, the Bengals have only George Iloka, Shawn Williams, Floyd Raven, Derron Smith and seventh-round rookie Clayton Fejedelem at safety.
However, there remains a chance that Leon Hall is re-signed and he could play both cornerback and safety. That's actually a role second-year corner Josh Shaw is set to take on in 2016, so the Bengals may roll with this group into the regular season, absent someone like Raven who's mainly a camp body.
Linebacker is even more deep with Vontaze Burfict, Rey Maualuga, Vinny Rey, Nick Vigil, P.J. Dawson, Marquis Flowers, Jayson DiManche, Karlos Dansby, Trevor Roach and Darien Harris, so it's not like those occasional linebacker snaps are there for Mays.
Even with the latest report, it's hard to see Mays re-joining the Bengals this year, though, it could be possible depending on how the regular season plays out.