The 17-second video posted on YouTube drew sharp condemnation from animal rights groups when it came to light in March.
The clip shows two Marines joking before one hurls the puppy into a rocky gully. A yelping sound is heard as it flips through the air.
"That's mean. That's mean, Motari," an off-camera Marine is heard telling the Marine who tossed the black and white dog. The off-camera Marine snickered slightly afterward.
Lance Cpl. David Motari, assigned to the 1st Battalion, 3rd Marine Regiment at Kaneohe Bay, is "being processed for separation" from the Marine Corps, the Marine Corps said in a news release. He also received unspecified "non-judicial punishment."
The Marine Corps didn't say what role Motari played in the clip.
"The actions seen in the Internet video are contrary to the high standards we expect of every Marine and will not be tolerated," Marine Corps Base Hawaii said in a news release. "The vast majority of Marines conduct their duties with honor and compassion that makes American people proud."
The second Marine, Sgt. Crismarvin Banez Encarnacion also received unspecified "non-judicial" punishment.
Encarnacion is assigned to the Weapons and Field Training Battalion, Marine Corps Recruit Depot San Diego.
First Lt. Binford Strickland, a Marine Corps Base Hawaii spokesman, said the service may not reveal what roles the two men played in the video because that was part of the investigation. He said releasing such information would violate the Privacy Act.
Strickland declined to provide details about the disciplinary measures taken against the men for the same reason.