We report on the observation of magnetic Feshbach resonances in a Fermi-Fermi mixture of ultracold atoms with extreme mass imbalance and on their unique p-wave dominated three-body recombination processes. Our systemconsists of open-shell alkali-metal Li-6 and closed-shell Yb-173 atoms, both spin polarized and held at various temperatures between 1 and 20 mu K. We confirmthat Feshbach resonances in this systemare solely the result of a weak separation-dependent hyperfine coupling between the electronic spin of Li-6 and the nuclear spin of Yb-173. Our analysis also shows that three-body recombination rates are controlled by the identical fermion nature of the mixture, even in the presence of s-wave collisions between the two species and with recombination rate coefficients outside the Wigner threshold regime at our lowest temperature. Specifically, a comparison of experimental and theoretical line shapes of the recombination process indicates that the characteristic asymmetric line shape as a function of applied magnetic field and a maximum recombination rate coefficient that is independent of temperature can only be explained by triatomic collisions with nonzero, p-wave total orbital angular momentum. The resonances can be used to form ultracold doublet ground-state molecules and to simulate quantum superfluidity in mass-imbalanced mixtures.