You can delete any song from a user created playlist by following these instructions:
- Navigate to Your Library > Playlists.
- Select the playlist you want to edit.
- Tap the three dots in the top right hand corner.
- Tap Edit.
- Tap the red circle next to the song you want to delete then tap Delete.
Swiping left on an individual song within your playlist does not remove it from the playlist, it only removes it from your Library.