But he doesn't even have a sword.
Why would he need one?
You can hit something hard enough and remove a limb. Plus, spoilers don't indicate even how he did it. Could have been a dragon claw or hints to his hybrid.
Im not arguing that there isn't potential for an unknown character doing it, but I doubt it at this point, it would have been a major spoiler and important to include.
Edit: Seemingly Kaido controls Wind, just like Thunder, so its possible he just cut her arm off with wind.