You’re probably not gonna like it, but since I went vegan, my grocery bills have decreased considerably. Aside from the cost of meat, cheese costs a ton as well.
Being vegan also reduces the amount of snack foods I buy (tho there are plenty of vegan-friendly snacks out there), so I’ve reduced my spending there. On the whole, there is a lot less spending on impulse foods and general garbage. I have also started baking my own snack cakes/cupcakes, tho I don’t know if the cost is less than a store bought item on sale. I think cooking your own food, as opposed to prepared items, is also a good way to reduce the cost.
My son lives with me and mostly eats what I make, tho sometimes I will make him a bunch of chicken breasts that he can add to the veggies/noodles/rice/potatoes with his dinner.
I’m not saying you need to go veg, but you might want to eat plant-centered meals a few times each week. And as others have said, sales and coupons.
One of my favorite cookbooks had many plant centered things. Although, for me animal products of some kind are an absolute must. Keeps me semi-sane and my name out of the news for going postal. :)