Please help us help you and fill where relevant:
Your LimeSurvey version: [see right hand bottom of your LimeSurvey admin screen]
Own server or LimeSurvey hosting:
Theme:
==================
As the title described, I have turned off the "no answer" option in the presentation setting but the "no answer" option is still there in the preview. What should I do? 

Please answer the questions about version, hosting, etc 

Sorry for opening this issue up, but I seem to encounter the same issue:
In my "Presentation" settings I set "show "no answer" to "off", but in my questions the "no answer" option (for non-mandatory questions) is still shown.

Version: 5.2.6+211213 Community Edition (self-hosted)
Theme: custom fruity variation

Please provide a small sample survey (.lss file).

Thank you for the quick response:
Below a survey with one (Yes/No) question.
Maybe I misunderstand the survey options. So let me quickly explain how I understand the settings:
I know that LS automatically inserts a "no answer" option when you set the question to "not-mandatory". In the past I always made the questions mandatory and just inserted my own "no answer" option. However, I find it more elegant to signal to the participant that some questions are mandatory and some are not. 
Anyway, I thought the settings in the "Presentation" section can change the behavior of non-mandatory questions "by setting the show "no-answer" to "on" or "off". However, in my survey (and in the attached sample survey) setting "show "no-answer"" to "off" does not seem to change anything for the behavior of the question.

 

It works as expected for me in version 5.3.5. I suggest you update to the latest version and test with a core theme.

Ok, thanks. Might be the version then. I'll update (probably tomorrow) and let you know how it went.

So I updated to 5.3.8.
My survey still shows the "now answer" option.
Maybe I am completely lost, but as far as I understood the option "show "no answer" in the "presentation" settings of the survey should change the behavior of non-mandatory questions. If the option is set to "on" non-mandatory questions by default have a "no answer" option (which is preselected, when running the survey). Wenn the option is set to "off" the non-mandatory questions should have no "no answer" option, or?
I also tried to adapt the "show "no answer" setting in the "presentation" settings of the global survey settings for all surveys. This also did not help.
Any suggestions? 

I face exactly the same issue, and I'm using the latest 5.3.9 version....