Also ein RTFM würde ja eigentlich reichen, aber weil ich ja nicht so bin hier ein Auszug aus der Mutt FAQ
How can I make Mutt use a SMTP server to send email, like Pine or [insert favourite Windows-based email client here]?
You can't. Mutt is a MUA (Mail User Agent), not a MTA (Mail Transport Agent). Other email programs include MTA functionality but the Mutt way is to use the proper tool for each task, instead of making a giant program that does everything. In short, it's not Mutt's job to get the mail to a remote SMTP server.
If your system does not have a properly configured MTA such as sendmail for Mutt to use, and you only need one to send all emails to a remote SMTP server for further delivery, then you can get sSMTP from ftp://metalab.unc.edu/pub/Linux/system/mail/mta/ and install that. sSMTP is easy to set up but very minimalistic, so you might want to check out nullmailer at http://www.em.ca/~bruceg/nullmailer/ instead. nullmailer can queue mails when the smarthost is down and then send them when it's up again.
Other MTAs and alternatives to sendmail are also listed in the Other Programs section on the Mutt Links page at http://www.mutt.org/links.html.