My answer needs base64 in addition to mail, but some uuencode versions can also do base64 with -m, or you can forget about mime and use the plain uuencode output...
FROM=me@mydomain.com
TO=someone@mydomain.com
SUBJECT="Auto emailed"
MIME="application/x-gzip" # Adjust this to the proper mime-type of file
FILE=somefile.tar.gz
ENCODING=base64
boundary="---my-unlikely-text-for-mime-boundary---$$--"
(cat <