Sometimes due to security policy you won't be able to use SMTP relay with sendmail service. The better way in this situation or in some other situation use Mutt 1.5.21 since in this version you can specify your SMTP server.
Steps:
1. Download and unpack Mutt 1.5.21
2. Configure it with SMTP option (root):
# ./configure --enable-smtp
# ./make install
3. Create .muttrc file (root or another user that you want to use):
$ cat /usr/local/etc/Muttrc > .muttrc
4. Find and update the following lines in .muttrc file:
set from="someuser@anydomain.com" - doesn't metter what will be here but something should be for correct work.
set smtp_url="smtp://mail.yourdomain.com:25" - here should be your SMTP server
NOTE!!!: if your SMTP is not pingable due to some security reasons then you should add it to /etc/hosts.
5. Create some file with any text.txt file that you want to send
6. Now send an email:
/usr/local/bin/mutt -s "Test e-mail" yourname@yourdomain.com < test.txt
That is all!