The launching process of a magnetically driven outflow from an accretion disk is investigated in a local, shearing box model which allows a study of the feedback between accretion and angular momentum loss. The mass-flux instability found in previous linear analyses of this problem is recovered in a series of 2D (axisymmetric) simulations in the MRI-stable (high magnetic field strength) regime. At low field strengths that are still sufficient to suppress MRI, the instability develops on a short radial length scale and saturates at a modest amplitude. At high field strengths, a long-wavelength clump instability of large amplitude is observed, with growth times of a few orbits. As speculated before, the unstable connection between disk and outflow may be relevant for the time dependence observed in jet-producing disks. The success of the simulations is due in a large part to the implementation of an effective wave-transmitting upper boundary condition.