The current-voltage characteristics of armchair graphene nanoribbons under a local uniaxial tension are investigated by using first-principles quantum transport calculations. It is shown that for a given value of bias voltage, the resulting current depends strongly on the applied tension. The observed trends are explained by means of changes in the band gaps of the nanoribbons due to the applied uniaxial tension. In the course of plastic deformation, the irreversible structural changes and derivation of carbon monatomic chains from graphene pieces can be monitored by two-probe transport measurements.