From the site:
The Mortality Schedules - In 1850, 1860, 1870, and 1880 census enumerators were directed to secure in addition to the usually required census data, information as to all persons dying within the 12 months preceding the census taking. These lists became known as the "Mortality Schedules".... The mortality schedules usually included the date and cause of death. Some online transcriptions do not include all data found on the original mortality schedule images. Hundreds of counties have been transcribed and and placed online.
There is only one mortality schedule on the site for New Mexico: from the 1885 Taos County census. However, more schedules may be added later. Also, it may be helpful if you looking for ancestors in other states.