With the script rm_tmbl.pl you are able to remove 50 posts from your tumblelog in one blow.

You can find this script in my github repo script-crap.

Why 50 posts only?
Well, the limit of posts you can retrieve in a JSON file from the Tumblr API is 50 posts per call. Don't believe me? read it for yourself. As limited as this seems, the workaround is to schedule(if you prefer with cron) the script. But not every minute, since the Tumblr API is slow, and it will only let you remove 50 post-ids the script just retrieved. I suggest scheduling to run every 5 minutes.

Note:
To retrieve all your posts-ids, and store them in a JSON file or HASH variable won't work. The API only lets you use a limited amount of delete requests, just like the posts retrieve limit. I'm not very certain about the correct amount, but I haven't tried more than 50 posts deletes per authentication.

The script makes use of the Perl Modules:

• WWW::Tumblr
• JSON::XS