The Exim home page says this about Exim:
The Exim Home Page
Exim is a message transfer agent (MTA) developed at the University of Cambridge for use on Unix systems connected to the Internet. It is freely available under the terms of the GNU General Public Licence. In style it is similar to Smail 3, but its facilities are more general. There is a great deal of flexibility in the way mail can be routed, and there are extensive facilities for checking incoming mail. Exim can be installed in place of sendmail, although the configuration of exim is quite different to that of sendmail.
If you don't have an internet connection, then you don't need an application which is intended to use the internet to fetch and send mail.
Disable or remove Exim. If there are problems such as other problems that will be removed along with Exim, apt will tell you so.
apt-get remove --purge exim
to remove it. Apt-get may ask for confirmation, and, as part of that confirmation message, apt-get will show you which other applications (if any) will be removed or broken. If it looks like removing Exim will cause problems, cancel the removal, then just disable Exim.
If apt-get doesn't ask for confirmation before removing Exim, then apt-get didn't detect any problem situation in re removing Exim.
Apparently you have Exim set up to start on boot. I'm not logged into my Debian installation at the moment so I can't tell you how to go about disabling Exim.