specific laptop model? there are many dv6 models. i have no way of knowing what internal gpu it has without you giving the specific model or by you saying what graphics card you have inside.
are you trying to play while plugged in to the wall socket or on battery? (by default the GPU is turned off and it uses onboard graphics when in battery mode which gives crappy game performance)
no you cannot insert a different graphcis card inside your laptop.
as pat mentioned above... perhaps the laptop is getting hot. that would explain a slowdown (performance throttled by high temperature alarm). some models get hot when you have them on your lap and need to be on a flat surface for cooling. some even need to be up on a stand for optimal cooling. this would be my second idea if you have it plugged in and your performance settings correct.