We have measured magnetoresistance of suspended graphene in the Corbino geometry at magnetic fields up to B = 0.15 T, i.e., in a regime uninfluenced by Shubnikov-de Haas oscillations. The low-temperature relative magnetoresistance [R(B) - R(0)]/R(0) is strong, approaching 100% at the highest magnetic field studied, with a quite weak temperature dependence below 30 K. A decrease in the relative magnetoresistance by a factor of two is found when charge carrier density is increased to vertical bar n vertical bar similar or equal to 3 x 10(10) cm(-2). Furthermore, we find a shift in the position of the charge neutrality point with increasing magnetic field, which suggests that magnetic field changes the screening of Coulomb impurities around the Dirac point. The gate dependence of the magnetoresistance allows us to characterize the role of scattering on long-range (Coulomb impurities, ripples) and short-range disorder (adatoms, atomic defects), as well as to separate the bulk resistance from the contact one. Based on the analysis of the magnetoresistance, we propose a more reliable method to extract the bulk mobility, which does not require prior knowledge of the contact resistance. It is thus demonstrated that studying magnetoresistance in the Corbino geometry is an extremely valuable tool to characterize high-mobility graphene samples, in particular, in the vicinity of the Dirac point.