The first things that come to mind as you haven't told us anything about the machine or setup is:
1. Inproper setup of the steps/inch ( these should be setup by actual measurement and not theroretical guess)
2. Backlash in the system. (your setting of z=0) and due to backlash, the tool is being "pulled into" the work. Could also be a collet that is not tight enough and it is being pulled out of the holder/collet.