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.　©　2017,　Chinese　Lasers　Press.　All　right　reserved.