What I lack in experience/knowledge about investing (I'm learning!) I make up for in grocery prowess. We spend about $80 a month for two people and a cat, and we live in Brooklyn so food prices are high, most of our couple friends have told us they spend about $250-$300/month (figure out those numbers if you want to pass out).
I don't buy any pre-made foods, and I make many condiments myself. That's where you're really losing money on groceries. You can make basically everything from fresh produce, bulk grains, bulk beans, bulk nuts. Meat is a treat for us. I make our almond milk, I make faux meats from scratch, tomato sauce from scratch, I freeze pesto, I freeze peppers, mushrooms, fresh cut corn, green beans, during the summer when prices are low and we eat them through winter. This way I am also not buying any commercial frozen food. I can tomatoes, beans, carrots, beets, pickles in the summer/fall. I make homemade gnocchi, sweet potato pasta, zucchini pasta, (so easy to do with a $25 spiralizer), pizza dough, sausages, dumplings, vegetable and meat stocks. For two dollars I can make about 12 cups of hummus- think about that versus commercial! Even the best sale in the world will NEVER get you close to the cost of most homemade foods.
Basically aside from produce the only items we buy commercially at a grocery store are: peanut butter, tahini, olive oil, ghee or butter, eggs, dried spices, molasses, bread, and cheese. The only real key to cutting down your grocery bill massively is to do as much as you can yourself, and avoid anything pre-packaged. People who wouldn't think twice about learning plumbing to fix a toilet scoff at the idea of making your own bbq sauce or pasta as being "crazy" or "too hard", but 3 cups of bbq sauce costs me about 20 cents to make, you can't even find that kind of deal at walmart. Oh, and the best side effect is that you won't want to go out to eat anymore, because your food will kick the ass of basically every restaurant anywhere.