I had been eagerly awaiting the ability to delete pull requests from bitbucket, only to find out there's a huge difference between bitbucket.org and bitbucket server. A community thread is involved with this: https://community.atlassian.com/t5/Bitbucket-questions/Delete-a-Pull-Request/qaq-p/74341
The feature has already been approved and implemented in server 5.1:
... and as that ticket states, there is nothing listed for bitbucket.org (which in itself should be a bug – the two should definitely strive to have similar feature sets!).