The ultra-short pule laser with the wavelength of 1064 nm and the pulse width of 10 ps is used as filamentation excitation source to induce the self-focusing effect inside sapphire creating a long filamentation trace, and the length of the filamentation trace breaks through the limitation of Rayleigh length. On the basis of different phases between filamentation region and the rest of the sapphire, we obtain fine cutting-surface of sapphire with roughness of 800 nm with the help of chemical corrosion. Arbitrary cutting paths can be achieved by this technique. The filamentation characteristics of picosecond laser and the processing parameters for the presented technique are studied. The laser power threshold of self-focusing effect is determined to be 2.78×106 W. The effects of picosecond laser peak power, focusing position and the number of pulses on the initial position of filamentation and cutting quality are investigated. The processing parameters for realizing high precision cutting of sapphire are obtained.