Greek drama kept violence off stage and out of sight. Acts of violence were usually narrated by the chorus. Maybe Shakespeare kept it off because that form of tragedy required it. (REASON AND WHY)
It is not evident that Shakespeare was following the Greek formula for tragedy. Some of the elements overlap, but in the end, Shakespeare did not often follow too closely any rules. He bent them, in fact. What one could make a good argument for is that this play (and many others...like Hamlet) are a hybridazation of the Greek tragedy with Artistolian influences, with new ideas and forms.