How do I remove a track I published to my profile?

To remove a song published to your profile, go to the profile view by tapping the profile icon at the top right corner of the home screen.

Then, tap the three-dot character "⋮" next to the track you want to remove and select "Delete" from the pop-up menu. This will only remove the song from your publicly-facing profile and not delete the project used to record it in your library.