There are clays,then there are clays that have little in common with other clays. I have lived and worked with black clay in N.Texas that will destroy your tractor and tiller before you turn clumps back to workable dirt,,,,,,,,,unless you go about it right. Assuming you are putting this in your yard,I'll tell you what works for my nasty black clay.
When wet it act's like bubble gum sticking to feet and tires until bulk weight literally "stop's you in your tracks". When dry,it shrinks leaving cracks 1"-3" wide and a few feet deep and become's hard as sorry concrete. The best way to pulverize clumps is to exploit the shrink-expand-shrink cycle. Use lawn sprinklers or alow rain to wet clumps and clods then wait until it dry's and cracks,at which point clumps will easily fall apart when desturbed. Use what you have (I like box blade) to begin placing soil where needed (not neccessarly leveling or smoothing). Why box blade work's well is that clumps can be rolled which help's to break them up. You will now have some well pulverized soil along with smaller clumps and clods which can be reduced to additional soil and even smaller clumps by repeating a wet-dry cycle. You can take more than one avenue here. (1) Attempt farthar busting with tiller (2) Sort everything larger than basketballs into piles and try tilling the rest. (3) Move usable dirt to fill selected area(s) that can be overseeded right away and continue processing clumps. Coming up on the wet season,it might become neccessary to tarp clump piles during rain to help them dry. If left til spring,the piles will break down but I suggest working it if it become's dry enough. Just keep in mind what I said about bubble gum when wet and don't mess with it. I suggest improving tilth by mixing compost,manure and wood chips as dirt is worked which will make final tilling much easier plus widen time window for moisture ussues.
Now,I have a rant. Everyone on TBN that own's a fel claim they can "back-blade" and do more and do it better than people with box blades. Construction operators do it every day and make it look easy but here's my challenge to weekend farmers. We put a pile of basketball size stones on one side of the lot then see who can move more to other side,back-blading fel or box blade. I'll spot the fel 5 secounds and loser pay's winner $5 each for differece in number of rocks moved within 10 minutes.