I like the answer above (with 0 votes; can't help, reputation = 1).
I was having exactly this problem, and didn't like the idea of temp and autosaves accumulating locally, even if offlineimap didn't sync them. What I did was prepend an rm statement to the mu4e-get-mail-command variable set in ~/.emacs.
This assumes you're using maildir format locally. So for me, with offlineimap and an otherwise typical GmailMailDir setup, this was:
(setq mu4e-get-mail-command "rm -f ~/.mail/\[Gmail\].Drafts/cur/*~ ; rm -f ~/.mail/\[Gmail\].Drafts/cur/cur/\#* ; /usr/local/bin/offlineimap -o")
in my ~/.emacs. This catches the temp files (affixed with ~) and autosaves (bracketed with #).
There are two drawbacks: 1. Your emacs buffer temp and autosaves for drafts will be deleted every time you check your mail. 2. If you have silly drafts already synced, they'll back-sync to your local repo (and not look like emacs buffer autosaves). I had to delete mine on Gmail.
If you wanted to "replicate" the better answer above in a Bash way instead of emacs, you could change this strategy to an mv instead of an rm.
mu4e-sent-messages-behaviorsetting ? The documentation doesn't have details, but it may get you started. ---------- Which server are you using ? The behaviour you are seeing, may be due to the server, rather than client (mu4e)draftname. But when I update-mail-and-index, the draft gets renamed (I guess offlineimap does that). So if I continue editing from the same buffer I started with, and save it again, a new filedraftnameis created. That file will be re-renamed again, to yet another name, and so on until you finally send the mail. So the more often you update-mail-and-index, the more drafts you get.