I'd wager neuropsych. The brain is one of the most complex things we have, and psychology comes from neurology. The mind and the brain are one, at least most clinicians would agree they are- so when it comes down the drawing the line between psychology and neurology, oftentimes it's realy blurry and it depends on what your lens is going in. So, some cases of stuttering will be deemed 'psychological' because maybe psychology therapies show some efficacy in management of them, and some will be deemed 'neurological' because it is through those therapies that some sort of management is attained. Things that have in the past been deemed purely psychological have shown neurological difference- neurochemical differences in depression, cortical mapping difference in conversion disorders, emotional regulation difference in borderline personality disorder etc. Brain and mind are instrinsically interlinked, so stuttering - which has psychological impact, and can be managed in some cases with psychological therapy, and which has neurolgical profiles and can be sometimes managed with neurological therapies - is neuropsychiatric/neuropsychological.