It's possible that it will root. Those little white bumps that form along the tomato stem are called adventitious root nodes - that means that were the tomato stem in contact with the ground, they would develop roots (the tomato is a vine after all, and vines can root at many points along its length.

Keep the tomato top in some water for now, and as soon as you have roots that are about 1mm long, plant it back into soil, and water it well for several days. If you are successful, the plant will be delayed in tomato production because it had to pause in its growing to form a new root system.

How big was your tomato plant? Cutworms usually go for smaller plants. Are you sure it wasn't a rabbit or some other larger pest? If you do have cutworms, it'll be a good idea to make some collars to protect your plants. You can use a toilet paper or paper towel tube, or a cheap disposable plastic drinking glass with the bottom cut out (the paper tubes will degrade and don't add to the trash you throw out, but they may not last long enough). Push it an inch or two into the soil and it will greatly reduce the number of chomped stems.

BP

Thanks for writing back so soon! The plant is a fair size as I bought it already partially grown from a green house. All the other plants have now been protected with a collar. It looks happy enough right now, and I'm stubborn enough not to give up on it. It wasn't a flush severing of the roots which is probably why it's taking on water so well, and it's in full sun. Is there anything else I can do to encourage root growth such as taking off some of the leaves on the bottom? Or what about putting some plant food in the water?
Any other info would be helpful.

I wouldn't put plant food in the water, but I would remove some of the lower leaves. It won't encourage root formation, but it will reduce the load on the plant - it's not as able to take up water right now as it was before so not having to support all the leaves will help it. Be sure to remove it from the water and plant it right away when you see roots forming - roots that form in water are quite different then roots that form in soil. It will just have to grow new soil roots and be delayed even further if you leave it too long in the water. About a week after you have planted it you can fertilize it.

It may still not root in time to save it, but it's certainly worth the try.

I would recommend you do a Google Image Search on cutworms so you know exactly what they look like, then go out and search over your remaining plants for anything that looks like that and squish it (or drop it into a can of soapy water if squishing isn't your cup of tea). You can sift through the top layer of soil for them and remove them. You can also treat with Bt (Bacillus thuringiensis) - it's safe to use around children and pets - it's a bacteria that's lethal to larvae (any good nursery should have it, but places like Home Depot aren't likely to know what you're talking about). And unless you're positive it was a cutworm, keep an eye out for bunnies or squirrels - my squirrels will chomp through tomato plants so I have to cover them with netting.

BP

My dog would be delighted if they actually came down to visit my backyard, so no it's not squirrels. Do you know how long it should take before I start seeing any root buds? I already have a fencing around my garden.