Most people in the US would say "get groceries" or "go grocery shopping."

This may be a regional thing. I'm from the northeast (USA) and I do occasionally say, "We have to do groceries." It's just shorter than saying, "We have to do the grocery shopping." Who has time for that 😂

I'm a US native speaker. "Do the groceries" does not sound right. However, everyone would understand it. You could say: 1) "I have to get groceries" 2) "I have to get the groceries" 3) "I have to do the grocery shopping" There's not much difference in meaning between the three. "Get groceries" suggests that you are about to make a meal and you need to get the ingredients for the meal. "Get the groceries" and "do the grocery shopping" suggests that it is part of a regular routine.

But you do the laundry and do the dishes. Why wouldn't you DO the groceries? I am asking because I am actually an English teacher. And an American friend told me the same as you. But I am a 100% sure I've heard it before. So I asked a few Canadian friends and they told me that they definitely say that. So I got super curious and this is why I am asking over here! :) I also asked a British friend who also told me that they don't usually say that!! haha

Thank you all for your replies. You've all been very helpful!!