Hi Jimmy, welcome to Outdoorking.
From the illustrated parts list it looks as if all three sprockets screw on. That necessarily means that the one on the engine/clutch shaft (a driving sprocket on a shaft that turns clockwise viewed from the far side of the engine) must be a right hand thread, and the other two (driven sprockets) must be left hand threads. They can usually be unscrewed without damage by use of a brass or hardwood drift against the bases of the sprocket teeth in conjunction with a hammer applied to the far end of the drift. You have to hold the engine/clutch shaft from rotating with a gas plier or Stillson. The reel can be jammed with a softwood plank. A rather nicer process involves wrapping the chain around the sprocket then gripping the outside of the chain using a Stillson with aluminium packers under the jaw teeth.
I agree that clutch does not look like the one in the parts list. I can't guess how it comes apart from this distance.