NFL teams have to cut their roster down to 75 by 4:00 p.m. EST Tuesday, August 27, 2013. The Titans must trim their roster from 90 down to the 75 player limit by then. By Saturday, August 31 at 6:00 p.m. EST they must get down to the 53 man roster limit.
Some teams have already begun the process of trimming their roster. You can keep up with the roster cuts for all NFL teams here.