I keep blowing fuzes after only a few seconds of operation.

I put in a new 15 amp fuze and the mower will start and run about 5 to 10 seconds before the fuze burns out.

I've place a test ligt between the battery ground and can't detect a short when the enging switch is off.

I've tried a 20 amp fuze but that burns out the ignition switch, wihich I replaced twice.

How can I find what is causing this problem?

Sounds like you have a bad ground somewhere.