$ sudo apt-get remove exim4 

Uninstall exim4 including dependent package

If you would like to remove exim4 and it's dependent packages which are no longer needed from Ubuntu,

$ sudo apt-get remove --auto-remove exim4 

Use Purging exim4

If you use with purge options to exim4 package all the configuration and dependent packages will be removed.

$ sudo apt-get purge exim4 

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 exim4 

See Also,