The clutch has nothing to do with the engine they work independently.
In neutral clutch is Engage, once engine is running gear box will all spin together and when clutch is disengage, Fork push on bearing push and bearing push on pressure plate will seperate clutch plate from Fly Wheel, hence gearbox rotation is slow down.
If using hydraulic clutch pump, service the clutch masterpump, clutch pump and change the fluid it could be overheated hyraulic fluid or better remove gearbox to change all clutch assemblies.