What tool is available for protecting the box cutter and the surface of the table while using box cutter?
Cutting mats are avilable in a wide range of sizes.  I have A4 and A5, but even A1 (59.4 x 84.1 cm or 23.3 x 33.1 inches) aren't expensive at around £/$/€20. They provide a reasonably non-slip surface (Link is to a UK shop, just happens to have a range on one page).

If you want even bigger, a layer or two of vinyl flooring can work in the short term, but you will get through that with a craft knife eventually, so its best mounted on scrapwood.

Another large, cheap option is hardboard (masonite), but it will blunt the blade faster than a proper cutting mat.  MDF is worse still, but either of these can be useful if you have a few very long cuts to make.