Delete songs completely

[slhourcade]

I have tried repeatedly to delete songs without success.  When a song is playing from "my music" I click the check and the X appears and a box comes up stating "removed from your music."  This does nothing.  The deselected song continues to play from my music and reappears later during the shuffle cycle.  The only thing that is changed is the green check mark is replaced with a plus sign.  I cannot delete any songs at all.  It's as if once you save a song to your music it is glued to you permanently- no options to completely rid yourself of the track.  It's really frustrating that something so simple as this appears to be so difficult to do.    I'm running Spotify premium on my Android phone and iMac desktop- it doesn't matter which device I use- the unwanted tracks continue to assault my ears.  Please help... : )