In this work, a direct-drive digital servo-press functioning with a non-conventional punch displacement profile was used to enhance the drawability of DP780 and TR780 steel sheet samples. Cup drawing tests were conducted under multiple detachments between the tools and the partially deformed part. The experiments were conducted with a special die set-up that provides a decreasing blank holding force scheme during the test. The results were compared with those obtained with the same die set-up but with a more traditional V-type punch motion, which continuously keeps the contact between tool and work-piece. The percentage of successfully drawn cups and the depth of the fractured cups were considered to evaluate the performance of this approach. In addition, two sets of friction tests were conducted with a flat die on a specially designed testing machine. The friction coefficient was measured as a function of the normal contact pressure, which varies spatially and temporally during drawing. FE simulations were conducted in order to explain the differences in experimental results obtained using conventional and unconventional punch motions. In particular, the roles of a variable friction coefficient as well as that of springback after detachment of the tool from the blank were investigated. It was demonstrated that the combination of these two effects successfully explain the higher drawing performance achieved using the attach–detach mode.