My only experience with stuttering was while I was recovering from post-stroke aphasia.

My speech therapist mostly suggested that every time I started to stutter I should stop trying to talk altogether, take a deliberate pause, and then concentrate on articulating... each... word... individually instead of letting my brain rush on ahead to the stuff I was about to say. Or, if that wasn't enough, articulating each syllable.

That worked pretty well, though it replaced the stuttering with a kind of slow monotone speech that was also kind of embarrassing.

Fortunately for me, the brain damage was temporary, so after a few months of this I started being able to speak more smoothly again. (Toastmasters helped a lot with that part, as did improv theatre classes.)

I have no idea if the same sorts of techniques would work for a less acute form of stuttering, though it seems like they ought to.

Edit Oh, and the other thing that helped was getting enough sleep.