I created a test Activity that installs a shortcut of itself on the Android Home screen. When you click a button, the Activity is supposed to remove the same shortcut it ju
While both solutions from Dev-iL and Funt work be advised they do so until Marshmallow. With Android 6.0 (which has Launcher v3) Google has removed the UninstallShortcutReceiver because of its security problems (probably because it became apparent here). So do not expect it to work with Android 6.0. Hopefully in some future release it will be readded in a form or another.
PS: Normally this should be a comment, but I am not allowed to comment because of the reputation...