If a spark is not obtained, inspect the motor wiring. As in a car, the ignition system uses the engine block as a ground, so make sure all the ring notches are tight and not loose. Damaged insulation can short-circuit the voltage to the engine block. The swords can be detached, and the screws holding the ring can be loosened due to vibration.
Check for loose or dirty connections.
The Kill Switch
If you still can't produce a spark, there might be a problem on the kill switch. This shuts off the motor by shorting the magneto coil and prevents a spark from being created when the mower is turned off. The switch works when you release the "Dead Handle" on the mower or put the throttle in the stop position. Trace The wire on the magneto coil to find this switch. You will most likely need to remove the hood from the top of the engine and possibly the steering wheel to check this.
Check the switch using the continuity or lowest ohm range on your meter. The switch must be in the open circuit when the engine is running and there is a shorting when the motor is off. Remove one of the connections to the switch when checking. Otherwise, the resistance of the magneto coil will give a false reading.