Lawn tractor won't do it, you need a rough mower. For just an acre you could use a walk-behind. They are rentable.
You want to mow right now when the brush is still dormant, knock it down to the ground while you can see what's what. It will come back, but as fleshy new growth, which you can mow again. If you hit it every few weeks you can use a regular lawn mower on that stuff. This time of year you can do surprisingly well just walking around with loppers and a saw. Cut off everything that's living at ground level. Pick up everything that's dead, plus what you just cut. Pile it all up and burn it. Pick up any rocks you can pick up and add them to the nearest wall.
If you're in NH I assume your soil is like mine, mostly rocks with a sprinkling of dirt between them. You do not want to disturb the soil, that will just bring rocks to the surface. If you have surface rocks the only tool that will survive is a string trimmer. That's a big area to cut with a trimmer. You want to limit yourself to cutting, mowing, burning and chemicals, no uprooting or moving dirt around. Trust me on this, I've broken three mowers in a day several times.
What kind of debris are you talking about? Is it rocks, logs, stumps, branches? Human-generated junk? Or just uneven ground? Rocks and stumps will break your mower, they need to come out. I don't like digging out stumps because I end up with a whole lot of rocks, so mostly I burn them when I can. Branches you can mow over with a rough mower. Logs won't generally break the mower but need to come out, pile them up and burn them.