We study the doping-driven Mott metal-insulator transition (MIT) in the periodic Anderson model set in the Mott-Hubbard regime. A striking asymmetry for electron- or hole-driven transitions is found. The electron-doped MIT at larger U is similar to the one found in the single band Hubbard model, with a first-order character due to coexistence of solutions. The hole-doped MIT, in contrast, is second order and can be described as the delocalization of Zhang-Rice singlets.