This is probably the easiest way to accomplish what you want. As has already been indicated by several people, you do not want to "export" as that will only create a wave file of the entire mix. It will not keep the individual tracks intact.
Basically you can select all the material just prior to the song you wish to keep by dragging your cursor in the time ruler. Just make sure all the tracks are highlighted. (Running the Edit > Select > All command first should insure this.) Once they are selected and highlighted, go to Edit > Delete (make sure the checkbox for "delete hole" is selected).
Once you have done this, you should save the project under a new name (e.g., Song 1), and then repeat the above described process to remove all the material AFTER the song you are working on.
So in short, it's select and delete all the material before the song. Save the project under a new name. Then select and delete all the material after the song and save again.
Repeat for Song 2, Song 3, etc.