I wouldn't say this was a bug, exactly. user:me is:answer hasaccepted:no is self-contradictory. A post can't both be an answer and have an answer (From the DB perspective, at least).
It might be nice if the search page gave you a warning, rather than just returning results that you don't want. But, accounting for all the possible contradictory search terms could be a low value-to-cost task.
user:me is:answer isaccepted:no works as it should.
What you want is more complex, and requires searching questions for one set of criteria while searching answers for a different criteria. For example, this would require two passes through the API.
To get this feature, you should make a Feature Request. Except that there already seems to be one: "Identify answers which might yet get accepted". You could support/upvote that post, too.
For immediate satisfaction, you can use the Data Explorer (SEDE). Just beware that the data is not live and can be up to a month old.
You can use my "My answers to questions that have no accepted answer" query until such time as this feature is rolled into the search page.
For example, SEDE currently shows that you have 59 answers to questions with no accepted answer.
