Translation:To kill two birds with one stone.
In the more peaceful Italian language (JK, no need to get worked up) we say: "[Acchiappare] due piccioni con una fava" = lit. [To catch] two pidgeons with one fava. But the two birds with one stone variation seems the most frequent one, you can even find it in Japanese: 一石二鳥 isseki nichō (one stone, two birds).
For those interested, apparently the "Two birds with one stone" variant of this idiom was initially (I'm assuming) based off of the exploits of Daedalus and Icarus of Greek myth.
this is an accurate illustration http://vaievem.files.wordpress.com/2011/02/2_coel1.jpg
In the UK we would never say "the same stone" only ever "one stone". Of course it makes sense and you'd be understood but... We are a bit lazy with language so the shortest way is the easiest. I'm super lazy so would just say "2 birds 1 stone" as the phrase is well understood.