The state officials began the process of removing the goats this week after plans were drawn up in June to relocate the goats into national forests in the North Cascades, their natural habitat.
The process is designed to protect natural resources, bolster the native goat population in the North Cascades and reduce threats to visitor safety, according to The Associated Press.
The officials estimate that 375 goats will be relocated during the venture. The park estimates that between 275 and 325 goats that can't be caught will eventually be killed.
Teams used tranquilizer darts to capture the animals before they are blindfolded, placed in slings and attached to a helicopter. After landing, they are looked at by vets, tagged and released into the wild.
The process is part of a year-long effort to rid the park of the animals.