What year and model Saturn?
Is the Check Engine light on?
Did replacing the throttle body have any effect on the problem?
Auto or manual transmission?
Does it just shut off or does it stutter/jerk and then stall?
Does it start right back up?
Does it stall at EVERY stop or just after you cruise for a little bit and then stop?
Ok, this sounds like your EGR valve is sticking partially open. You can remove it fairly easily to have a look. I recommend replacing the gasket while you have it off. You should be able to push the center pintle in easily with your finger and it should pop right back out. If it is hard to push or does not pop all the way back out and make a good seal then you can try cleaning the EGR valve pintle. Also, disconnect the battery during this process.
I usually use an old tootbrush and some carb cleaner spray. You can spray some in a small container and then put the valve in facing down like it is installed in the engine. Then let it soak for a while. You only need 1/4 to 1/2 inch of cleaner in the container to work against the carbon buildup on the pintle. After it soaks scrub it with the toothbrush or other item to remove the carbon. When it looks clean and moves easily install it back on the engine with the new gasket.