Sounds like you're referring to collected songs rather than a playlist. However, I'll include steps for both just in case.
Go to My Collection and tap the name of the playlist you'd like to edit. Then, you can remove songs from one of your playlists.
Tap the Edit icon below the album art.
To remove songs scroll down and press ( X ) to the left of the songs you would like to remove or swipe the track name left.
To adjust the order of your playlist, hold and drag the list icon on the right of the track title to the desired position.
Tap Saveto close out and save your changes.
Removing Collected / Saved Songs:
You can remove a playlist/album/song/podcast from your mobile device.
Go to My Collection and select Playlists/Albums/Songs/Podcasts (depending on what you are looking to remove).
Next, tap the highlighted check mark to the left of the play icon to remove it from your collection.
At this time, you won't be able to remove multiple saved songs in bulk. You would need to remove individual songs. You also have the option to remove an album, if you no longer want to have it in your collection.