The formation of a local zone of Cdc42 GTPase activity, which governs cell polarization in many cell types, requires not only local activation but also switch-off mechanisms. In this study, we identify Rga3, a paralog of Rga4, as a novel Cdc42 GTPase-activating protein (GAP) in the fission yeast  Schizosaccharomyces pombe  Contrary to Rga4, Rga3 localizes with Cdc42-GTP to sites of polarity. Rga3 is dispensable for cell polarization during mitotic growth, but it limits the lifetime of unstable Cdc42-GTP patches that underlie cell pairing during sexual reproduction, masking a partly compensatory patch-wandering motion. In consequence, cells lacking  rga3  hyperpolarize and lose out in mating competition. Rga3 synergizes with the Cdc42 GAPs Rga4 and Rga6 to restrict Cdc42-GTP zone sizes during mitotic growth. Surprisingly, triple-mutant cells, which are almost fully round, retain pheromone-dependent dynamic polarization of Cdc42-GTP, extend a polarized projection, and mate. Thus, the requirement for Cdc42-GTP hydrolysis by GAPs is distinct during polarization by intrinsic or extrinsic cues.