Offal.

Seriously. Offal is just brilliant. Extremely cheap and nutritious as well as being the perfect "Caveman food" - if you can stomach the idea of it. Pun not intended.
People really seem to overlook offal, which is a damn shame - a beef heart is so similar to (and perhaps even nicer than) a steak. Kidneys are brilliant sliced up and fried like sausages... You can do all kinds of stuff with what average, overly squeamish people throw away - let them have their boneless, skinless chicken breasts; we get the real feed. ;D

Since eating more primal, we have cut ouyr $200 a week grocery bill, to $120 a week. Thats for four hearty eaters!! A little planning goes a long ways!

Agree, I find paleo cheaper. I did buy a 1/4 cow, but grass fed isn't required for all meat. (just really good).
Since I don't buy boxes of food that have been processed and driven across the country, I get real food from farmers nearby. (either at my store or farmers market).
Another great idea is the crop share. A box of veggies every week for a fixed price each month. a fraction of the cost of processed food.

We're spending around $100/week now in groceries, which is pretty amazing. Until we get our cow portion (probably going in on it with some friends) we go to Costco and stock up on stuff. Trader Joe's is also very helpful, and I scour sale and the "used meat" (bargain) bin at the grocery store-- found 4 organic free range chickens a couple weeks ago The biggest thing for me is planning-- that's the most helpful, and I've had to do that a lot more.

I hate to say this, but it needs to be said: healthy food is not 'cheap' and some spending re-prioritization may be needed.

We have been raised (especially in the US) with cheap food - but like just about everything else, that food is cheap because the manufacturers cut corners, use inferior components - and produce in massive scale. When you look at growing organically, using old-school fertilizers and pesticides, etc. It IS more expensive - but that is the ACTUAL cost of nutritious, healthy food. Organics and free-range are inherently more expensive than factory-farmed and feedlot, and it's a concept that we all have to accept and get used to. Drop Starbucks, or HBO or whatever.

That being said, I use all the tips above to trim costs...

- most meat prices fluctuate depending on if a new catch is in or a new generation is entering the slaughterhouse. An example: wild-caught salmon normally runs 12.99/lb around here, but when the new catch starts to flood the distribution pipeline, the price drops to 7.99/lb for a couple of weeks. When that happens, I buy several full fillets and stick them in the freezer. Yeah, it costs money - but I've also saved almost 50% over the next couple of months. The same happens with beef, poultry and pork - learn when the prices momentarily drop and have some money set aside to take advantage of it.

- buy the cheaper cuts of meat and learn to use slow-cooker 'braising' methods. Steaks and roasts are my favorite, but they're also the most costly. Stew meat, OTOH is my go-to: I can make stews, soups, chilies etc. Whole chickens are cheaper than parts: I roast the bird and get four meals out of it: wing/leg/thighs make one meal for me and my wife, breasts makes a second, then the carcass goes into the pot and soup is made for two more meals. Take a pork roast and crock-pot it into pulled pork, and you've got another three meals: a whole week for two people using two cuts of meat.

- the same ideas can be used with veggies: buy what is in season and is grown locally. Every crop has a drop in price when it first floods the market; that's also when they're freshest and most nutritious. Buy what is on special and eat a lot of it, then buy what's on special next week and eat a lot of THAT. Blanch it and freeze a bunch for when it's NOT cheap.

- grow your own. Tomatoes can be grown on a patio; so can chard. Four chard plants can produce for two all summer (by picking just the outer leaves, the roots keep growing new leaves in the center). Zucchini and cucumbers are notorious big producers

I don't know if its an option for you, but I'm going with deer meat this year to try and save some money. I'm getting a couple hunting tags for bow and gun season and a friend of mine's husband (who absolutely loves hunting) said he'd be happy to fill the tags for me and help me get the meat all cut up and packaged. I grew up on venison and it's a great filler for soups and stews and stir fry. I think the tags are only going to end up costing me around $50 total for at least two deer, and then making sure I have enough freezer bags and freezer paper to accommodate the meat.

cheap cuts of meat such as: oxtails, liver, ground meat, other organ meats would be great. Also, up your egg intake if you need a stretch at the end of the month. Also, buy whole chickens and, after you eat all of the meat, make a chicken stock out of the carcass. Find ways to stretch what you have. Otherwise, I always find my grocery bill goes up significantly when I start buying the packaged foods that tell me I am straying from a good paleo diet.

I do not find Paleo to be cheaper than a regular SAD diet... my grocery bill has gone up about $50/week. The grass-fed organic meat seems to be the bulk of the extra cost. I have done research on what non-organic fruits and veggies are safe to buy, and which ones need to be organic. Whole Foods has really good deals on cage-free organic eggs and bacon. I love their 365 brand! I think one of the previous posters hit it on the head... our society does not appreciate healthy, organic, whole foods quite as much... the healthier foods are just more expensive.

I speaks so poorly to our society when organic cucumbers cost more than a burger and fries at McDonalds.

I think we'd be doing much better health-wise as a society if even a quarter of those ginormous corn and wheat fields were used for a solid rotational farming of other veggies. It's no surprise that those cucumbers are so much more expensive when there are heavens-knows-how-many times more corn fields than anything else growing.