One technique I specifically find quite helpful is to take three (short) breaths in, and one long, slow breath out. Followed by correctly saying the sentence that had tripped me up to begin with - sometimes slowly or with emphasis, depending on how badly I tangled it. I've been using this technique so long I've forgotten where I found it, it works quite well for me. Especially since it may not always be easy to step aside for a moment, as Alex Common mentioned.
This is a thoroughly unnatural breathing pattern, and takes a bit of concentration to boot, so it helps give a bit of distance and breathing room (ha!) from the conversation. Between that and getting that darn sentence right, it usually calms me down enough to start speaking correctly again. Speaking a bit more slowly and taking a little time, even half a second, to plan how I want to say my point helps keep it from happening again.
You may find other breathing patterns or self-distraction techniques useful, as well as or instead of what I described. Even a single deep breath may be enough to help. Or else maybe closing your eyes, and/or making some slow hand gesture, just somehow distracting yourself from the conversation for a second, just long enough to slow yourself down a bit. You can also look up meditation breathing or techniques, for visualizations to pair with such an exercise or other ideas that might speak to you better.
As a disclaimer, I don't stutter myself so can't say how it may or may not be useful for that, specifically. I tend to use it because when I get overexcited I skip words or tangle my sentences, and generally trip myself up - and then get flustered, which doesn't help me untangle myself.