It would appear that deleting your own post doesn't actually do anything from the mobile site.
I just had a little mixup- I prematurely posted a question (by hitting return on my phone when editing the title, possible another issue of its own) but I stopped the page load, so it didn't appear that I had actually posted anything.
When I had finished typing the question (but hadn't posted it), I then noticed the premature question that I had accidentally posted, which had been down voted and closed. From the mobile site, I hit the delete button under the question content, as I wanted to delete it. It prompted me for confirmation, and I click yes, and the page refreshed. The question remained, but I assumed I was just voting like the people who closed my question. (The confirmation prompt actually says Vote too) I then went on to create a new question, with a near identical title to the premature one, and the correct body content.
I was then informed that I had posted an extended duplicate, and was told to edit the previous post. So I did just that, and tried deleting the duplicate I had just posted (from full site). To my suprise, the post was almost immediately removed...