The solution is simple and it's actually embedded in the game's options
Team Fortress 2 is a free-to-play FPS produced by Valve and it was launch on Steam for Linux a while ago, but some users have reported problems with the framerate.Even if Valve has pushed a lot of updates for Team Fortress 2, one particular problem hasn't been resolved. Some users reported stuttering, even if they met the required hardware configuration for the game.
The solution came from one user on Reddit and it also made its way into the official ValveSoftware github channel.
It seems that disabling “Multicore Rendering,” which is on by default, has solved the stuttering completely and a lot of users have reported an immediate improvement.
More details about this issue can be found in the Reddit thread.
You can also download Steam for Linux 184.108.40.206 right now from Softpedia.