You should read the book! I'd do a TL;DR but I can't really remember the specifics other than John really hated the distraction of pretty much anything.
Seems Google, Reddit (u/Ungard at [1]), and Amazon [2] have all the answers. Turns out it was Carmack with the ax. An excerpt from the book:
This happened after Romero accidentally locked himself in his office. Hearing the pleas, Carmack gave the knob a twist, paused, then deduced the most obvious and immediate solution. “You know,” he said, “I do have a battle-ax in my office.” Carmack had recently paid five thousand dollars for the custom-made weapon—a razor-edged hatchet like something out of Dungeons and Dragons. As the other guys gathered around chanting, “Battle-ax! Battle-ax! Battle-ax!” Carmack chopped Romero free. The splintered door remained in the hall for months.