How do I tell Mutt to not store sent messages?

Just to make it a litte more clear: in /home/user/.muttrc:

set copy=no

There's the copy option to control if copies of messages you sent are saved. It's a quadoption, so can be set to no (which would accomplish what you want), yes to save messages automatically, as well as ask-yes or ask-no to have it ask on each message with you being able to choose the default.

I managed to do this with:

set record = "/dev/null"

From what I read there a lot of options for granular control. record being one of them. When copy is set to no all storage of mail copies is disabled. Whereas the record variable can be overridden by the $force_name and $save_name variables, and the "fcc-hook" command. see the manual

Technically I am misusing it in my example since it only specifies a save path. But it does give you more control by being able to override it with other variables.

However you did ask for a specific record value that would do the job ;-)