In order to feed a family of 4 on 75$ of food per week you need professional cook level and a big freezer.
Early fall you need to prepare and freeze yearly portion of tomato sauce, apple sauce and vegetable and fruit puree or cake, etc.. (all vegetables and fruits that cost nearly nothing when open market close mid fall). End of summer you buy big portion of strawberries, blueberries, leek... chopped them off and freeze them in ziploc.
You need to buy your non perishable stuff (everything that is not meat/fruit/vegetables/dairy product/bread) at big markets like Costco. Cereals, pasta, rice, couscou, broth, etc...
You need to look for big rebates on meat. Look for pork and chicken when on sale. Buy big portion. Prepare many different marinade and cut portion so you can put them in marinade again in ziploc bag and freeze everything (labels your ziploc so you will read what it is a month later!
).
Learn to make salads or vegetables dish out of current vegetables that are really cheap depending on the season.
Buy only frozen juices.
Avoid and be very careful on your buying of dairy product and bread. No more buying bottle water!
I do think it is possible if you are a real good cook that can plan things. If not it's not possible. Not on a yearly basis.
Cheers,