I would suggest a scrap backer.
Are you cutting one side of the box at a time or stack cutting 2 or more sides at once? (I usually clamp the front and back together or the two ends and cut two at a time.) You may get some tear out but, only on one piece and if you use a piece of thin plywood as a backer you will probably save both pieces and they should match fairly well.
If you orientate the pieces corectly, the tearout should be on the inside of the box and alot easier to hide.
Sometimes poo poo just occurs. The true test of a good wood worker is the ability to hide the goofs.
I don't make mistakes, I just have design changes once in awhile.
Rog