Wont delete music

I downloaded a playlist from itunes and I decided I didnt like it so I wanted to delete it but when I swiped from left to right to delete it is gives me the delete sign and when I click that it just makes the song have a sign on the sign that looks like the icloud download sign. So when Im playing my music the song wtill comes up. Ive tried everything to delete it but it wont delete. Does anybody know how to permanently delete it? Thank you.