There has recently been a great deal of interest and excitement in applying graphene field effect transistors (GFETs) in digital and radio frequency (RF) circuits and systems. Peculiar output characteristics such as kinks and negative differential resistance (NDR) in a strong field are the unique transport properties of GFETs. Here we demonstrate that these unusual features are attributed to a carrier sheet density constrained transport framework. Simulation results based on a simple analytic model which includes the linear DOS structure are in very good agreement with experimental data. The kernel mechanism of NDR is ascribed to the fact that the total current increase of a channel with a high average carrier density is constrained by its minimum sheet density. Utilizing in situ Kelvin probe force microscopy (KPFM), the principle which naturally distinguishes NDR from kinks is further verified by studying the spatially resolved surface potential distribution along the channel. The influence and potential application of GFETs' unique output characteristics in the digital and RF fields are also proposed.