Yes, you can use stuff you cut and dry yourself. HOWEVER the tricky part is getting and keeping it dry enough that it does not get moldy. Also it will take up more storage space than baled hay or straw (because you cannot compact it the way a baler does).
I would suggest trying it but with maximum attention paid towards drying it super thoroughly before storing and then storing it in a way that will minimize chance of dampness problems (it needs to be able to 'breathe', don't plan on sealing it into bags or piling it up against a wall), and then see what happens. A lot depends on your particular situation. If you can get it to work well enough for you, great; but be prepared for the possibility that it may get fungusy and you may need to buy something after all.
Note btw that most people consider hay/straw harder to spot-clean in a coop than shavings (not an issue if all your cleaning is total-cleanouts, of course) and the sort of material you'd be cutting (finer, like hay, not coarse like straw) is the sort of material from which some people have had issues with impacted crops. OTOH lots of people use hay without having problems.
Personally I think the best way to economize on bedding is not necessarily to go for the 'free' stuff -- which can be very high maintenance and not necessarily work as well, although there are exceptions) -- but rather to devise management strategies that minimize bedding replacement PERIOD. Droppings boards, for instance, will save you a good bit of bedding.
Good luck, have fun,
Pat
