NO, it is not finished.
The anime finished before the manga:
Anime finished: October 24, 2008
Manga finished: September 27, 2012
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
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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Anime - Base
Release date: October 09, 2003
Anime - Sequel
Release date: January 08, 2008
Anime - Sequel
Release date: October 24, 2008
Gunslinger Girl explores the lives of young, traumatized girls in Italy who are given a new lease on life through cybernetic enhancements by a government agency.
However, this second chance comes at a steep price: they are brainwashed and trained to become assassins.
The story follows these girls as they navigate the complexities of their new identities, grappling with their emotions and desires for connection within a world that demands they be emotionless killers.
The anime focuses on their struggles to find meaning and purpose, and the ethical implications of using children as weapons, all set against the backdrop of political intrigue and violence.