In this paper, we study Hawking radiation as a massless particles tunneling process across the event horizon from the Schwarzschild and Reissner-Nordström black holes pierced by an infinitely long spinning cosmic string and a global monopole. Applying the WKB approximation and using a generalized Painlevé line element for stationary axisymmetric spacetimes, also by taking into account that the ADM mass of the black hole decreases due to the presence of topological defects, it is shown that the Hawking temperature remains unchanged for these black holes. The tunneling of charged massive particles from Reissner-Nordström black holes is also studied, in both cases the tunneling rate is related to the change of the Bekenstein-Hawking entropy. The results extend the work of Parikh and Wilczek and are consistent with an underlying unitary theory.