Another Marine with the battalion remains in critical condition.
The investigation into Tuesday's crash is ongoing, military officials said in a statement.
The region where the accident took place is just over the state line and west of Fort Bliss, a major Army installation in West Texas that has played a critical role in dispatching military deportation flights and served as a touchpoint for thousands of soldiers and pieces of equipment now deployed along the border.
The troops are deployed there in support of President Donald Trump's executive order to secure the U.S.-Mexico border.