Making MOSFET switch faster
Ignoring the poor attempt at a circuit, you are actually switching off current when you turn your MOSFET off but, because the LED will go high impedance you are left with a circuit node with parasitic capacitance that is charged to nearly the same voltage at which the LED operated at.

Without any "load" resistance this voltage will dwindle away quite slowly. The parasitic capacitance will be several hundred pF and is due to the MOSFET drain-source capacitance and the LED parasitic capacitance.