Gator clutch belt

I've been reading different forums and am still unclear if the belt should be turning all the time-even when the gator is in neutral. As you might guess, I'm having the traditional issue of grinding gears, on my second clutch, but now I must stop the engine, start it then quickly put into gear. I have to kill the engine each time I move from neutral to either forward or reverse.

Waiting for a magic answer

and yes, I have the idle as low as it will go.