So... is Break Blade finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: June 22, 2014
Manga finished: October 12, 2022
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Break Blade is set in a world where people can manipulate quartz for various uses, but a war is brewing between the Kingdom of Krisna and the nation of Athens.
The story centers on Rygart Arrow, an unusual individual who is completely unable to use quartz, making him an "un-sorcerer."
Despite his inability, Rygart's unique nature unexpectedly makes him the key to piloting an ancient and powerful Golem.
This Golem becomes Krisna's last hope against the advancing Athenian forces, placing Rygart at the heart of the conflict.