You can delete songs from the database only by using the Delete option on the Song menu.
Deleting a song is a permanent step you cannot undo a deletion.
If you don't want to permanently delete the song from disk, you can instead select [Archive Song] from the [Song] menu.
Archiving a song will move it to a new folder named [Archive], stored within the default [Worship Songs] folder. This way, if you change your mind later, you can import the song back into the database.