Pizza pan materials vary, some are stronger than others. A pizza wheel cutter will damage your pan depending on the durability of the pan material. For instance, ceramic or steel pizza pans, have low chances of getting a single scratch.
Other factors include whether the pizza pan is nonstick or coated. The wheel cutter may not have any effect, depending on the strength of the coating. If the layer is weak or wearing off, then the pizza cutter will leave a mark.
It is best to set the pizza aside before you start slicing it up. That way you’re essentially protecting your pan. Putting it on another surface also eliminates the risk of the pan sliding if it has a very smooth bottom.