The reason why the "iTunes cutting" does not work might be because you cannot cut a song in iTunes, only change the start and stop time (kind of trimming)
In GarageBand you use the standard editing/trim tools to cut a song.
Just out of curiosity, do you ask this question because you cannot find the explanation in the GarageBand manual or do you expect other users to read the Manual for you so you don't have to?
welcome to the Apple Support Communities!
It is not quite clear from your question, if you are asking about GarageBand on your MacBook Pro or GarageBand on an IOS device (iPad, iPhone)? For you posted in the GarageBand for IOS forum, but your "Profile" signature says MacBook Pro?
If you want to know about GarageBand on your Mac, start from the GarageBand Support page: http://www.apple.com/support/garageband/
- Here are some easy to follow Video Tutorials:Video Tutorials
- Most help is accessible from the "Help" menu in the GarageBand main menu bar: Click the "browse Help" button and look at the part "Create a Song Arrangement", i.e. the section "Arrange Regions in the Timeline": Split and join regions:
If you are asking about GarageBand on your iPad/iPod, the online manual is here:
Again, see the section on "Edit Regions" on how to trim, split, and cut regions: Edit regions
Good luck for your project!