The blade adapter slips over the crankshaft before the blade goes on. The blade adapter is not pressed on or secured by a pin or set screw. After time the blade adapter becomes rusted to the engine crankshaft and can be very difficult to remove.
You probably already have the lawnmower laying on the side. If not drain the fuel and oil and place the lawnmower on it's side. Spray the blade adapter liberally with Liquid Wrench, or some other rust buster. Tap down and up on the edges of the adapter with a hammer. The vibrations will help the rust buster penetrate between the blade adapter and the engine shaft. You might need to let the lawnmower set and reapply the rust buster and tap several times to break the adapter loose from the engine shaft. The blade adapter will eventually come free and you can remove it.
If you have a gear puller, screw the bolt that holds the blade on into the engine shaft so that 3-4 rows of thread are inside the shaft. Install the gear puller so the driving bolt of the puller is pushing on the bolt and the jaws are gripping the top edges of the blade adapter. The gear puller will remove the blade adapter from the engine shaft.