It won't come up as a new blog post via notifications if you only edit an existing blog. As long as there's not going to be loads of them at once, the best way to get a blog deleted atm is to simply flag it yourself - it also helps to edit it to ask for deletion in the blog content. This will put it in the mod queue and as long as the flag is by the poster and it's clear you want it removed a mod will delete it for you upon seeing it in the queue.
I don't know when or even if a feature for users to delete their own blogs in currently planned, but editing to ask for deletion and flagging your blog/topic/etc yourself is a quick and concise way of getting our attention and making sure we know you want it removed.
Yeah that's dumb not to have a remove feature. I made a blog about GTAO being boring. The notifications didn't work properly so I thought after a month or so I had no comments, so I tried to delete it but no dice. Since I couldn't delete it, I changed to ask "why people play Barbie's Horse Adventure?" just because I couldn't delete it. After editing it, I noticed I did have a comment. Glitch Spot and all that. The user said something like "I didn't find it boring and I enjoyed it". So now it looks like he was commenting on Barbie's Horse Adventure.