Hi I have taken IELTS recently and although my stutter is pretty bad usually I managed to go through the speaking part fluently. I gotta say the guy was super profesional even giving me hints with hands when I spoke for too long which was perfect. In the end I got 8.0 from speaking, can you imagine that? :D If you are nervous about your speaking part why dont you try some of the great lecturers on [Preply](https://preply.com/) I bought a few lectures there for a really great price as my lecturer was from South Africa and I think it really helped me in the speaking part as I was prepared for the challenge and was not scared of the english itself. Also as much as I dont like to use my stutter as an excuse, it might be wise to consult some people from IELTS/TOEFL administration about your issue as I believe you should be given some concession i.e more time and also your stutter will be then accounted with and should not be used against you. So if you have to get some super high score I would recommend you to use this path.