Using a Mosfet correctly as a switch in this circuit and how to prevent it from "loading"? the circuit
It cannot work like that. The mofet discharges the capacitor just down to the value where VStaircase goes a bit lower than Vsine, not down to zero as you wish. It's a negative feedback, that it should do. 

To act as you wish you need to trigger a short impulse that fully opens the mosfet for a short time.