Justice Gregory Carro ruled there was "insufficient" evidence that Mangione's actions were intended to "intimidate and coerce a civilian population."
Prosecutors had argued the terrorism charges were appropriate due to the targeting of a prominent CEO and the public nature of the shooting.
Despite the dismissal of the terrorism charges, Mangione still faces a second-degree murder charge and eight weapon-related charges in New York.
He is also facing five charges in Pennsylvania, including forgery and carrying a firearm without a license, as well as federal charges of interstate stalking, firearm offenses, and murder through the use of a firearm.