It will be difficult to use the belt as a clutch due to the slack required to allow it to slip...It will end up falling off the vertical pully...Three options come to mind:
1. Use a centrifugal clutch on the shaft of the lawnmower, and modify it to have a pully instead of sprocket
2. Use a centrifugal clutch on the axel....This is much more complicated as you must modify the clutch so that the output side is now the drive side. I don't recommend this.
3. Use a jackshaft with a clutch on one side (connects to the axel) and a pully on the other side (connects to engine). This is the approach I would take.