CNC milling of curved surfaces is a common task in the manufacture of molds and dies of products used in various industrial sectors. Notably, in recent years, the use of hard milling has helped manufacturers to obtain these parts with shorter lead times, since the part is machined in a single setup without the problems caused by part distortions from the tempering process. In this work, cylindrical surfaces were machined in AISI H13 steel tempered and annealed to 52 HRC using hard milling and high speed milling concepts in the finishing stage. The cutting tool was feed along either upward ramping or downward ramping directions, and the quality of the texture of the obtained surfaces was evaluated as well as the wear of the ball nose cutter. The results showed that the surface is deteriorated when milling is performed in the downward direction (surface roughness equal to 6.93 μm) compared with the upward direction (2.17 μm). Also, vibration marks are present on the machined surface in the downward direction. In addition, surface roughness is worsened when the tool performs the cut primarily at regions away from the center of the tip of the ball nose cutter. On the other hand, the surface roughness is worsened when cutting with regions near the center of the tip of the ball nose cutter when milling in the upward direction. It was noticed that flank wear in both upward and downward directions was low (less than 10 μm), and micro-chipping was observed in the cutting edges.