Well, I haven't been vegan for very long, but I've been vegetarian (no dairy) since the beginning of the year, and I watch my grocery bill pretty closely so maybe I can help? Here are some things that I've been doing to help cut grocery sticker shock. As it is, my family of 4 (2 adults, 2 toddlers) spends about $100 a week on groceries.
Do you have grocery flyers each week with sales? I plan meals using the sale flyers and weekly specials. If there's a sale on something we use often (canned black beans, canned tomatos, etc) I stock up when they're on sale.
I tend to buy fruits/veggies in season. For example, right now items like tomatos, sweet corn, onions, melons, and different types of lettuce are in season so that's the bulk of my fresh fruit/veggies. I can usually get those types of foods in the winter, but they're much more expensive. Fruits/veggies that are grown locally seem to be a better deal too, so I check out the farmer's markets as much as I can.
When I need a little variety at a lower cost, I turn to the freezer. I'd much rather have fresh, but in the middle of winter it's tough to find much variety in fresh produce.
I shop around to some extent. With gas prices I don't go from store to store as much as I used to, but some items are cheaper in certain stores. I buy bulk when I can for things like rice and beans.
Does any of this help? I know there's also a frugal board on this forum that you might want to check out, too.