Looking here for an API endpoint to delete and/or rename a piece of content in a repository. I don't see anything relevant. How does one do this? https://developer.atlassian.com/bitbucket/api/2/reference/
Unfortunately, in May 2017 Atlassian stated that it is not supported.
When looking at the Bitbucket REST API of version 5.10.1 in June 2018, it is still not supported.
There is a files endpoint at /rest/api/1.0/projects/{projectKey}/repos/{repositorySlug}/files, but it only has a GET endpoint to list the files in a specific directory of the repository.
There also is a /rest/api/1.0/projects/{projectKey}/repos/{repositorySlug}/browse/{path:.*} endpoint. It supports GET to list the files in a directory of a repository and supports PUT to commit one file per call. However, DELETE is not supported on that endpoint.
The same goes for renames. The documentation does not mention the ability to do so with a REST API call.