Tapping mode atomic force microscopy (AFM) is employed for dynamic plowing lithography of exfoliated graphene on silicon dioxide substrates. The shape of the graphene sheet is determined by the movement of the vibrating AFM probe. There are two possibilities for lithography depending on the applied force. At moderate forces, the AFM tip only deforms the graphene and generates local strain of the order of 0.1%. For sufficiently large forces the AFM tip can hook graphene and then pull it, thus cutting the graphene along the direction of the tip motion. Electrical characterization by AFM based electric force microscopy, Kelvin probe force microscopy and conductive AFM allows us to distinguish between the truly separated islands and those still connected to the surrounding graphene.