When you say "delete" are you asking about removing a song from a playlist or completely deleting it off your computer?
If you want to delete it from a playlist, but not off your computer, while viewing the playlist, right click and select "Remove From List". As an alternative, you can click on the song, bring up the tag and scroll way down to the playlist it's on and uncheck the box. You can also add tracks to a playlist this way. Another alternative is to click/highlight the track and hit the "Delete" key on your keyboard. This only removes it from you playlist.
If you're wanting to completely (as you say) delete the file while in the playlist view, I don't think you can. You can under "Files" view. It's probably a protection.