Papyrus is a well-known braggart, but in a quarrel, his humble nature manifests despite his will. It’s mentally impossible to damage such a bunny!
Not willing to lose his hero status, he may send a few bones towards you. They’re easily omitted, but if you want to play into Papyrus’s hands, you’ll see how concerned he is about your wellbeing. When you remain with the only point of health, he authoritatively stops the battle until you fully restore. A couple more unlucky attempts and the caring skeleton will let you continue the game without a fight.