If these are sweetgums you are talking about, you will need to treat these to keep from resprouting - maybe more than once, as they are very tenacious.
You may want to try lowering your cutter and cutting perpendicular to the original cut - this might help take some of the remaining stalks out and would more than likely splinter the rest - You will still have stobs to deal with.
If you are looking for immediate clean results a dozer may be your best bet, but more than likely you will still have resprouting unless you first treat existing stalks with herbicide.