Cutting the bolts might not be the best solution. Closet bolts are typically made of brass which does not rust. However, there can certainly be other types of corrosion present, as well as dirt, grime, and mineral deposits if water got in there (you do need to replace the wax ring, after all). This means that the nuts are likely not fused to the bolts, but just need some encouragement to break loose.
Before attempting to remove the bolts, I recommend spraying them with a product such as Penetrating Blaster.
Let it soak into the area around the nut for a minute or two. Next, get a socket wrench and pick the smallest socket that will fit over the nut and torque it free. If you cannot get the nut to move, try using a breaker bar which provides more leverage. If you do not have access to a breaker bar (you really should have one and they do not cost a lot), you can improvise with a box wrench and a narrow metal pipe slipped over the handle (cheater bar).
Cutting those bolts would be further down on my list of options. In order to keep the toilet firm on the floor without rocking back and forth the bolts should be moderately tight. Cutting through one of them may cause a sudden shift of weight which may cause damage such as cracking the porcelain near one of the bolt holes, or the saw blade may nick the enamel coating on the toilet. If you must use a saw, I would prefer a rotary tool such as a Dremel with the proper metal-cutting blade. Be sure to wear both gloves and safety glasses, move anything flammable away from the work area, and cover trim, drywall, anything nailed down that you do not want damaged. This will create a lot of hot sparks.