I'm surprised there is a clutch on an electric saw. There is a centrifugal clutch on petrol saw so that the motor can idle. There is a "kick back" brake on all saws, the purpose is to instantly stop the saw if it kicks back. It's linked to the reset lever on the top side of the saw, there is a weight on this calculated to trip the brake. (This is the thing you pull back to reset the brake.) It's connected to a switch to simultaneously turn off the power when it operates. You need to test the motor and the switch operation while the chain& bar is removed, ideally with an electrical continuity/resistance meter.
When an electric motor (with carbon brushes) operates intermitantly, it's sometimes the case that a single circuit in the armature is open circuit. If the motor happens to come to rest with the brushes on this circuit, it won't work. The clue is lots of sparking at the brushes and a burnt segment on the commutator. Also if you move the armature slightly it runs. In this event you need a new armature or these days, it's likely to be junk. TURN THE POWER OFF BEFORE YOU MESS WITH IT :-)