Use Winamp to spit it out to a WAV format file and then use a wave editor to split into multiple WAV files. Then re-encode each WAV to an MP3 using Lame (or Razorlame for the GUI version).
To my knowledge, there is no good audio editor that will edit compressed mp3 files. Nero's built-in wave editor can decode .mp3 files for editing automatically, but it can only re-encode at 128 kbit/s.