Final machining steps are commonly requested on parts obtained via additive manufacturing to ensure the required surface finish and geometrical tolerances. When machining additive manufactured workpieces, their typical microstructural anisotropy is rarely taken into consideration. In this work, the influence of the build-up orientation of Ti6Al4V parts obtained via laser powder bed fusion on machinability is studied. Ti6Al4V blocks with horizontal and vertical development were additively manufactured and then milled. Tool wear progression was monitored and its effect on surface quality investigated. The cutting tool that machined the horizontally oriented sample showed a tool life 66% higher than the one that machined the vertically oriented one. This study demonstrates the strong correlation between the build-up orientation of additive manufactured components and their machining response.