If you are site admin, do the following:

• Go to: YOURSITE.COM/admin/content/node
• Select "Type" is "Blog" and then click "Filter"
• Check the blog writings you want to remove
• From "Update options" select "Delete" (or what ever you want to do for the checked items)
• Click "Update"
• You're done

OR... use "Advanced Search" at:
YOURDOMAIN.COM/search/node
...to find the blog items you want to delete, and then edit&delete them one by one.

If you're not the site admin:

If you're not the site admin and want to delete blog posting(s) it really depends how the site admin has set up the "Access Control" (Access Rights) of the site. If that's the case, just contact the site admin.

Hope this helps...