How do I change the tempo without speeding or slowing any of the live tracks I've recorded? I set the wrong tempo and when I try to modify it the vocals sound really slow.

See my first screenshot:

The "Follow Tempo and Pitch" flag is in in the Track Editor. Click the scissors icon in the Toolbar of the GarageBand window, to reveal the Track editor. Then select one of your recorded regions.

In the Track editor click the "Region" tab.

If the "Follow Tempo and Pitch" flag is not visible, enlarge theTrack Editor window by dragging the dividing line to the track area upward.

What is yourGarageBand version?

Basically you need to disable "Follow Tempo and Pitch" for all recorded regions that you want to keep unchanged, when you change the tempo of your song.

In GarageBand 10.0

Or in GarageBand '11: