We study the forced aspiration of small (approximate to mm) and large (approximate to cm) liquid drops, deposited on prewetted porous membranes, and pumped mechanically with a constant current J. Two kinds of membranes are used where the pores are i) disconnected, cylindrical and calibrated or ii) interconnected "sponge-like". Whatever the size of the drops and the intensity J of the current, two suction regimes are observed versus time: 1) a "locked" regime, when the drop is pinned, with a dynamic contact angle decreasing from advancing (theta (a)) to finite receding (theta (r)) contact angle; 2) an "unlocked" regime, where the contour line recedes with a constant contact angle closed to theta (r). In both regimes, the shape of the drop remains quasistatic, during the suction process, i.e. a spherical cap for small drops and a flat "gravity pancake" for large ones.