Yes. Eating vegan can be a lot cheaper than eating meat/dairy.
The only reason vegan can be expensive is when people buy a lot of mock meats, cheeses etc. which aren't even that good for you anyway.
If you cook using wholefoods then it is very economical

I cook with lentils a lot and use them in the place of vege mince in spag bol, lasagne, pies etc. They also make good curries.
Rice is good and can be used to make a healthy pumpkin risotto or fried rice with lots of veggies, garlic, ginger and soy sauce.
Aldi is awesome for tinned foods and other bacics (I bought a whole heap of fruit, veg and tinned stuff the other day which only cost me $30), and food markets and fruit shops. Try to avoid shopping at places like Woolworths and Coles as their prices are usually more expensive.