In the concluding few sentences of Foundation and Empire, the Mule says that:
I call myself the Mule - but not because of my strength, obviously -
They do not finish the sentence. Earlier in the book some Foundation denizens theorised that it was because of his hard-working attitude to galactic conquest (which seems odd in itself), but this effectively disproves that. If it was not because of his strength, why did he name himself thus? I presume that it's implied but I have failed to make any inferences.