In terms of loss of life, it was almost certainly the wars involved in the expansion of the Aztec Empire from 1428 to 1521. These wars were carried out not only for political expansion but also to obtain victims for human sacrifice. (Sacrifices were also a tool of political intimidation and terror.)
The numbers are disputed but some authorities have put the toll of human sacrifice (most of the victims being captives obtained in warfare) in central Mexico as up to 250,000 victims per year. It is alleged that the number of victims sacrificed at the consecration of the Great Pyramid at Tenochtitlan was over 80,000 (although other estimates are as low as 4,000). The Aztecs also engaged in what were called Flower Wars in order to obtain captives for sacrifice.
Any conflict between tribes north of Mexico would have been trivial compared to these battles.
The Incas also engaged in major wars during their expansion from 1438 to 1533, but these would have certainly been much less lethal since the Inca did not engage in mass human sacrifice of prisoners as the Aztecs did.
There were major military campaigns during the expansion of earlier empires in Mesoamerica and in the Andes, as well as conflicts among the Mayan city states. However, since the populations and empires involved were smaller the battles probably were as well.