In addition to the well established global HI-deficiency seen in Virgo cluster spirals, many of them are found to be HI-deficient in their inner disks. We show that collisions between galaxies in a cluster can lead to the preferential removal of HI from these galaxies. This follows directly from the application of the Spitzer-Baade collisional gas removal mechanism to galaxies consisting of stars and a two-component ISM of HI and H2, with HI having the largest filling factor. This can account for both the observed Hl-deficiency in the inner disks of these galaxies as well as their normal H2 contents. The frequency of galaxy collisions in the Virgo cluster is shown to be large enough to make collisional gas removal a viable mechanism.