Until now, humanitarian demining has been unable to provide a solution to the landmine removal problem. Furthermore, new low-cost methods have to be developed quickly. While much progress has been made with the introduction of new sensor types, other problems have been raised by these sensors. Ground-penetrating radars (GPRs) are key sensors for landmine detection as they are capable of detecting landmines with low metal contents. GPRs deliver so-called Bscan data, which are, roughly, vertical slice images of the ground. However, due to the high dielectric permittivity contrast at the air-ground interface, a strong response is recorded at an early time by GPRs. This response is the main component of the so-called clutter noise, and it blurs the responses of landmines buried at shallow depths. The landmine detection task is therefore quite difficult, and a preprocessing step, which aims at reducing the clutter, is often needed. In this paper, a difficult case for clutter reduction, that is, when landmines and clutter responses overlap in time, is presented. A new and simple clutter removal method based on the design of a two-dimensional digital filter, which is adapted to Bscan data, is proposed. The designed filter must reduce the clutter on Bscan data significantly while protecting the landmine responses. In order to do so, a frequency analysis of a clutter geometrical model is first led. Then, the same process is applied to a geometrical model of a signal coming from a landmine. This results in building a high-pass digital filter and determining its cutoff frequencies. Finally, simulations are presented on simulated and real data, and a comparison with the classical clutter removal algorithm is made.