No injuries were reported in Sunday's disturbance.
The Dona Ana Sheriff's Department says about a dozen inmates who were in one pod of the jail and were given the clippers to cut their hair had refused to give back the shears and became disruptive.
Inmates in nearby pod also became disruptive and used a broom handle and piece of metal broken off a desk to break several windows.
Another inmate started a fire in a trash can and lit a few mattresses on fire using a lighter he had in his possession.
A sprinkler system inside the pod put out the fire.