You can delete a playlist station by following these steps:
1) Go to the top level of My Stations and then tap on the station you would like to edit.
2) Once you are viewing the list of shows in the station, tap on the station name at the top of the list.
3) You will get a context menu that includes Delete Playlist
4) Once you tap Delete Playlist, you will be asked if you want to permanently delete. Tap Delete or Cancel accordingly, to complete.
You cannot delete the default Favorites Playlist or the Live Radio playlist (if there are live stream stations saved in Live Radio).