What I can buy at the local dollar store (everything is $1 each item) that is vegan:
dried beans (have found Great Northern white beans, pintos, and black beans in this section in a 1 lb bag for a buck)
canned beans (have found chickpeas, pintos, black beans, kidney beans)
diced tomatoes and tomato sauce
cans of applesauce
frozen fruits and vegetables (usually in three to four serving packages) (have found blueberries, mango, strawberries, peaches, mixed vegetables, corn, and green beans)
3 serving box of raisins or 6 pack single serve boxes
bag of sunflower seeds (raw) and bag of salted pumpkin seeds with shell on and no other ingredients listed
Westsoy plain lowfat soy milk in 32 oz carton (made with whole soybeans, labeled organic, and 4 servings)
corn flour for making your own tortillas (also happens to be certified gluten free)
instant plain oats in canister
distilled vinegar
Lemon juice although it has lemon oil listed on it
used to get plain canned pumpkin there but haven't seen it lately.
This is all I can think of off the top of my head. I have been doing some shopping there and saving a bit of money. For some reason the exact same brands of some of the items I am getting at the dollar store (such as Goya beans) I can find at regular supermarkets but they are more expensive by sometimes as much as $0.40. Dried white beans are more expensive at the supermarket by almost a $1. I realize some of this stuff at the dollar store is not organic and some is off brands but when you are on a budget you do what you can.
At the supermarket I buy my produce, potatoes/sweet potatoes/squashes, whole grains such as rice, millet, bulgur, steel cut oats etc, tofu or tempeh (not every week but twice a month or so), or a few specialty items like salsa, cocoa powder, or some spices.
I might spend a little more on high quality oil but rarely use it so I might buy it once every other month if I do some baking. I buy vegan butter maybe once a year at Christmas lol. I get my nutritional yeast, chickpea flour, and buckwheat groats in bulk at my local Whole Foods Coop since I can't find them elsewhere but again buy those items every two or three months. I make my own bread if I eat it. Used to buy Ezekiel bread but stopped buying it altogether about a month ago as it is way too expensive. Other than the soy milk from the dollar store I stopped buying commercial plant milks and make my own flaxseed milk which is still cheaper than store bought milk (1/4 cup flaxseeds and six cups water yield five cups milk). I stopped buying fancy sweeteners like agave, maple syrup, turbinado sugar etc a while ago and just use applesauce or fresh fruit or raisins or something. I also grow my own stevia herb plant and use stevia leaves for when I blend my flaxseed milk or make smoothies. If I bake a large batch of something on special occasion I have been buying beet sugar (American Crystal Sugar made in Minnesota) and a bag of that will last me three or four months (would last longer but my husband uses it for his stuff).
I think the more expensive vegan food items would be Earth Balance, vegan cheeses and spreads such as Daiya or Tofutti, processed fancy organic cold cereals, organic nuts and seeds, (though flaxseeds can be fairly cheap as can sunflower), fancy oils (coconut, high end organic canola or olive etc), sweeteners, some organic and high end plant milks like hemp or rice, organic vegetable broths, frozen meals like Amys and processed boxes of mixes like Fantastic Old World or McDougalls soups, and the fake meats like Field Roast or tofurkey or Beyond Meat. Or condiments like vegan worcestershire sauce and tamari and so on. These items I almost never buy. I get the impression that non vegans think these items are predominantly what vegans eat. Often in "starter kits" for vegans and vegetarians these are exactly the types of items listed.
On a side note, when you think of the cost of agriculture in terms of feeding farm animals (which means growing a lot of grain or providing vast space for grass fed animals), providing shelter for them, vet care, labor to care for them and milk them etc, antibiotics, and the cost, energy, and labor to slaughter the animal and process it into edible meat, to me this seems like a much greater cost all around than simply growing plants for us to eat directly. There is still cost for space, labor to process them, and water needed etc but with animal agriculture there is the need to grow plants AND the animals. I just don't see how animal agriculture can possibly be more efficient and cost productive than plant based.