How can I disable the iPhone's microphone? I would like to disable the internal microphone for everything. My device is jailbroken and I have tried 'Disable Microphone' in MyRepoSpace, however that just gets rid of the Voice Memos app instead of actually disabling the microphone.

Is there a way to disable the microphone, such as deleting the drivers? Or do I have to physically break it?

Deleting mediaserverd from launchdaemons removes all audio and recording. However, it also makes the device hang for several seconds when something tries to play audio.
If security is a major concern, I'd assume that a software hack is not the solution. There still is a chance of malicious software importing code which re-enables the audio functionality. 

I read NSA guidelines for Mac OS X 10.6 about disabling iSight on Macs where is was recommened to physically remove the webcam for absolute security.

If you do not want to physically remove your iPhone's microphone, I would try to distort the audio as good as possible - that would leave a spy with imprecise mumbling noises. The iPhone 4 can be muted quite effectively by just closing the hole at the bottom. There is a good chance that closing the hole of the microphone has the same effect. You could apply prestik or hot glue for example.