In this paper a signal processing technique is developed to reduce clutter due to ground bounce in ground penetrating radar (GPR) measurements. This technique is especially useful when a GPR is used to detect subsurface anti personnel mines. The GPR clutter is modeled using a simple parametric model. Buried mine and clutter contributions are separated through a set of iterative subspace projections. The algorithm outperforms existing clutter reduction approaches and also yields target features which are useful for detection and identification of these mines. It is shown that the proposed technique increases the probability of detection and at the same time significantly decreases the false alarm rates when combined with a matched filter detector.