Open the full length mp3 in audacity. Use the selection option at the bottom of the screen to choose the first clip
copy (cmd+c), file new (cmd+n), edit paste (cmd+v)
export as mp3 with your new clip name, repeat for the other clips.
edit: this is assuming you already have the lame encoder, and used it, if not you'll need to download that and will have to point to it the first time you export as mp3