Short answer: no.
Deletions on this site are soft-deletions. You cannot delete posts in a more firm way than you already did. Deleted posts will stay visible to you, moderators and users with sufficiently many points. Moreover, these posts can have an impact on the account, e.g., they can contribute to automatic posting-restrictions.
In very exceptional cases posts can be disassociated from an account. They would then be no longer linked to the account that asked them. This is however more common for undeleted posts.
If you posted something that absolutely must be firmly deleted, for example to disseminate the information would create some major risk or concern, say, you accidentally posted confidential data, then moderators have tools to deal with this (flag the post and explain the situation).
Regarding the trash-bin emptying analogy. The user-interface makes it quite difficult to even get to ones own deleted posts, especially to older ones. In that sense the bin is emptied.