The best way to find a cheap train ticket from Zürich Hbf to Stuttgart Hbf is to book your journey as far in advance as possible and to avoid traveling at rush hour.
This is the last train of the day.
Find all the dates and times for this journey
2 h 58 m
3 h 1 m
Trains per day
Of the 6 trains that leave Zürich Hbf for Stuttgart Hbf every day 4 travel direct so it’s quite easy to avoid journeys where you’ll have to change along the way.
Here are some other resources that might have the information you need