Can I use a mosfet to discharge quickly a capacitor without resistor?
This is not a good idea. It may work OK if the capacitor is very small. But you will be operating the transistor in a pulse mode and you will have to refer to the peak pulse power allowable from the datasheet. It is always better to dissipate heat with a resistor rather than with silicon. Even a small resistor (a few ohms) will likely completely shift the power dissipation from the transistor to the resistor. Try to choose a resistor with a pulse power rating listed in the datasheet. Also, you may want to put a fuse in series so that if/when the mosfet fails, nothing catastrophic occurs. MOSFET's usually fail short.