Secondary Tumblr blogs can be deleted from the settings page of the blog in question. Unlike primary blogs, secondary blogs can have multiple members; if the Tumblr you wish to erase has other members besides yourself, you must remove them first before you delete the blog otherwise it will keep running with the remaining members.

Deleting Blogs

Click the Settings cog icon at the top of the dashboard, then select the name of the blog you want to deactivate. At the bottom of the page, click the Delete button. Confirm your choice on the confirmation screen, re-enter your username, password and the blog URL and the blog is deactivated.

Removing Members

If you see a Leave button rather than a Delete button at the bottom of the blog's settings page, the blog has other members. From the dashboard, choose the blog from the drop-down menu on the right, then click "Members." From the subsequent screen you can remove the other users associated with the blog. After this is done you can deactivate the blog in the normal way.