A multi-scale analysis of the capillary instability of Newtonian liquid ligament is presented. The DNS code ARCHER calculates the temporal evolution of the ligament subject to a capillary instability for two initial wavenumbers. The analysis of the process is performed with a multi-scale approach initially developed to investigate liquid atomisation processes from 2-D visualisation images. In the present work, the axisymmetric condition allows performing a 3-D analysis also. The analysis reports three characteristic scales that divide the scale space in three regions. In each region, specific scale dynamics is found illustrating the involvement of different mechanisms. In particular, the characteristic small scale reports three regimes of decrease corresponding to the known dynamics of the neck of a contracting ligament until breakup occurs. Furthermore, the existence of a pure elongation mechanism during the process is identified. This mechanism limits the overall surface area reduction associated to the capillary instability. The evolution of the elongation rate of this specific mechanism appears to be equal to the one of the small scale evolution rate