This is on an iPhone 5C running 8.1.3.
Swiping to the left to delete a track is insanely difficult. What I did...
Step 1: Settings-->Music-->deselect "Show All Music", then deselect "iTunes Match"
Step 2: Settings->General-->Usage-->Manage Storage-->Music-->Edit (upper right corner of the screen)
Once you select "Edit", you should get delete buttons beside all the data in the app. In my case, it listed several audiobooks, each with its own delete button, followed by "Tracks" and it's delete button, followed by "Artists" and it's delete button. When I deleted the tracks, the artists disappeared too.
See if that works for you.