Additive manufacturing induces a microstructural anisotropy in its components, that reflects on their mechanical properties, and, in turn, on their machinability. In this paper, the tool wear when milling laser powder bed fused Ti6Al4V parts with four different build-up orientations was evaluated. The tool wear was qualitatively and quantitatively examined, and assessed indirectly by analyzing the chip morphology and the machined surface quality. This study demonstrates that the tool life decreases gradually up to 40%, going from machining horizontally manufactured samples to vertically manufactured ones. Furthermore, a novel interpretation of the correlation between the tool life and the additive manufacturing-induced anisotropy of the part was given.