You can uninstall or removes an installed budgie-core package itself from Ubuntu 16.10 (Yakkety Yak) through the terminal,
$ sudo apt-get remove budgie-core
If you would like to remove budgie-core and it's dependent packages which are no longer needed from Ubuntu,
$ sudo apt-get remove --auto-remove budgie-core
If you use with purge options to budgie-core package all the configuration and dependent packages will be removed.
$ sudo apt-get purge budgie-core
If you use purge options along with auto remove, will be removed everything regarding the package, It's really useful when you want to reinstall again.
$ sudo apt-get purge --auto-remove budgie-core