How do you manage conversations when you're doing something physical?

How do you manage conversations when you're doing something physical? When I know I'm going to stutter, I can sometime take a moment to gather myself, and focus on the words so that I minimize how much I stutter. I can't do this when I'm doing something physical like working out, or playing a sport. I've been doing BJJ for a while and I've noticed that I am not grounded enough when I'm breathing fast and my heart rate is high, so then I try to rush through my words when I know a stutter is coming, and that makes it worse. Its usually when I have to introduce myself, or explain something when I'm already winded. How do you guys deal with these situations?