Yes, but can he cut through a ship with a sword in one hit?
*Edit: in seriousness, I think one of the difficulties in defining the Mundane vs Supernatural is the sliding scale. If one consideres cutting through a ship is just barely supernatural and fitting of a high level "mundane" fighter, cutting the heads of everyone within 15 feet probably sounds really mundane.
That precise squishiness is why I've tried to write the question off for years, and just get everyone using some agreed on power-source. You have to first solve the aesthetic problem, which you're never going to get perfect consensus on but you can probably get close enough to do design work; where is the line between
amplifying a mundane trait and creating a new ability? People (including me!) generally will forgive the former, but object to the latter. Mundane abilities generally cannot be "techniques," self-contained bundles of rules that are invoked by themselves. Instead, you need to take a universal rules construct, (making attacks, climbing stuff, lifting heavy things, etc.) and amplify that.
The next problem once you've done that is the issue of generalizability. The problem you run into then is making sure the scaling is consistent; because you're not describing a discrete, self-contained action, but instead using the action to showcase a general property of a character, you need to ensure whatever ultimately ability you get is generalizable to similar situations. Lifting a large rock to do a big thrown weapon attack necessitates lifting heavy doors, necessitates stronger basic attacks, necessitates bending steel and so on.
The source material tends to fail you here. Myth and legend usually showcase specific feats of strength or ability, but don't then build on them to establish consistent truths about the character.
Thinking about it, the task would be significantly easier if the basic resolution system for mundane tasks integrated a currency from the get go. If you were spending focus or effort or exhaustion or something as part of normal skill checks, it would be much easier to expand on and appropriate the resource for use with limited high level techniques.