Do you have PhysX set to higher than 'low' in your video settings? If yes, try setting it to low as you might have a large performance hit due to the fact that the PhysX would be CPU-bound if you have an AMD GPU. (Source: PC Gaming Wiki; Borderlands 2 - PhysX)
I'd also try setting the framerate option to 'Smoothed 22-62'. What it does is try to maintain your frame rate between 22-62, automatically adjusting the engine (graphics, effects, draw distance, etc) on-the-fly, to try to maintain this frame rate in parts where your PC starts to drop the frame rate below the minimum (22fps). Source: Steam forum post on 'Capped 60, smoothed 22-62, or unlimited+vsync on?' thread
If that still doesn't work for you, try changing the framerate setting to 'Unlimited' instead. Then, try changing MinDesiredFrameRate from 35 to 60 in WillowEngine.ini in the USERS directory: C:\Users\%USERNAME%\Documents\My Games\Borderlands 2\WillowGame\Config\. It may result in the expected performance from high-powered hardware. (Source: PC Gaming Wiki; 'Borderlands 2 - Microstutter on Powerful Rigs')