I don't recall having any gastro problems as a child, or being anxious to cause it. I was anxious, I know, cos I used to bite my fingernails (not done so for over 20 years now.)
I am not a health expert, so these are just my ideas.
If your child does have gastro problems cos of anxiety, then try to calm them down. Maybe with a toy they like, or singing if that's what they like doing. Get their mind away from what is going on with their body to something they enjoy.
For older children to adults. There are two ways that help me at times, that you could try.
1. Deep breathing exercise that can be called 'the 4-5-4'. You breathe through the nose to the count of 4, hold for 5 seconds, then breathe out of your mouth to the count of 4, relaxing as you go. Do that a few times. I have done this on a bus to go shopping to calm my anxiety so I didn't have to dash to the toilet.
2. Mindfulness. I was taught this in CBT. I usually do it in bed at night. I lie down, arms at my side, breathing in and out calmly. I tense my feet for a few seconds then release, then my legs, working my way up to my head. Then I loosen my body so I'm relaxed enough to turn over and go to sleep. It is meant to work.
I hope these can be of help to your autistic child.